Sets Venn Diagrams Competitive Exams
100 questions · Mathematics
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Question 1 of 100
In a group, 42 people like tea, 25 like coffee, and 11 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 42 + 25 - 11 = 56. Tip: Subtract the intersection so it isn't counted twice.
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Question 2 of 100
In a group, 27 people like tea, 40 like coffee, and 11 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 27 + 40 - 11 = 56. Tip: Subtract the intersection so it isn't counted twice.
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Question 3 of 100
In a group, 30 people like tea, 40 like coffee, and 18 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 30 + 40 - 18 = 52. Tip: Subtract the intersection so it isn't counted twice.
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Question 4 of 100
If a set contains 8 elements, how many proper subsets does it have?
ExplanationProper subsets formula is (2^n) - 1. (2^8) - 1 = 255. Tip: The set itself is not a proper subset, so subtract 1.
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Question 5 of 100
In a class of 51 students, 40 play cricket and 39 play football. If every student plays at least one game, how many play both?
Explanationn(A ∩ B) = n(A) + n(B) - n(A ∪ B) = 40 + 39 - 51 = 28. Tip: Both = (Sum of individual) - Total.
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Question 6 of 100
In a group, 45 people like tea, 26 like coffee, and 13 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 45 + 26 - 13 = 58. Tip: Subtract the intersection so it isn't counted twice.
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Question 7 of 100
If a set contains 3 elements, how many proper subsets does it have?
ExplanationProper subsets formula is (2^n) - 1. (2^3) - 1 = 7. Tip: The set itself is not a proper subset, so subtract 1.
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Question 8 of 100
In a class of 93 students, 51 play cricket and 54 play football. If every student plays at least one game, how many play both?
Explanationn(A ∩ B) = n(A) + n(B) - n(A ∪ B) = 51 + 54 - 93 = 12. Tip: Both = (Sum of individual) - Total.
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Question 9 of 100
In a group, 40 people like tea, 26 like coffee, and 21 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 40 + 26 - 21 = 45. Tip: Subtract the intersection so it isn't counted twice.
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Question 10 of 100
In a class of 65 students, 30 play cricket and 55 play football. If every student plays at least one game, how many play both?
Explanationn(A ∩ B) = n(A) + n(B) - n(A ∪ B) = 30 + 55 - 65 = 20. Tip: Both = (Sum of individual) - Total.
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Question 11 of 100
In a class of 70 students, 54 play cricket and 33 play football. If every student plays at least one game, how many play both?
Explanationn(A ∩ B) = n(A) + n(B) - n(A ∪ B) = 54 + 33 - 70 = 17. Tip: Both = (Sum of individual) - Total.
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Question 12 of 100
In a class of 68 students, 33 play cricket and 38 play football. If every student plays at least one game, how many play both?
Explanationn(A ∩ B) = n(A) + n(B) - n(A ∪ B) = 33 + 38 - 68 = 3. Tip: Both = (Sum of individual) - Total.
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Question 13 of 100
In a class of 51 students, 41 play cricket and 33 play football. If every student plays at least one game, how many play both?
Explanationn(A ∩ B) = n(A) + n(B) - n(A ∪ B) = 41 + 33 - 51 = 23. Tip: Both = (Sum of individual) - Total.
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Question 14 of 100
In a group, 35 people like tea, 27 like coffee, and 20 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 35 + 27 - 20 = 42. Tip: Subtract the intersection so it isn't counted twice.
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Question 15 of 100
In a class of 66 students, 33 play cricket and 50 play football. If every student plays at least one game, how many play both?
Explanationn(A ∩ B) = n(A) + n(B) - n(A ∪ B) = 33 + 50 - 66 = 17. Tip: Both = (Sum of individual) - Total.
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Question 16 of 100
In a class of 55 students, 36 play cricket and 49 play football. If every student plays at least one game, how many play both?
Explanationn(A ∩ B) = n(A) + n(B) - n(A ∪ B) = 36 + 49 - 55 = 30. Tip: Both = (Sum of individual) - Total.
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Question 17 of 100
In a group, 30 people like tea, 34 like coffee, and 16 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 30 + 34 - 16 = 48. Tip: Subtract the intersection so it isn't counted twice.
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Question 18 of 100
In a class of 40 students, 36 play cricket and 34 play football. If every student plays at least one game, how many play both?
Explanationn(A ∩ B) = n(A) + n(B) - n(A ∪ B) = 36 + 34 - 40 = 30. Tip: Both = (Sum of individual) - Total.
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Question 19 of 100
In a group, 22 people like tea, 29 like coffee, and 6 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 22 + 29 - 6 = 45. Tip: Subtract the intersection so it isn't counted twice.
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Question 20 of 100
In a group, 41 people like tea, 40 like coffee, and 14 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 41 + 40 - 14 = 67. Tip: Subtract the intersection so it isn't counted twice.
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Question 21 of 100
If a set contains 4 elements, how many subsets does it have?
ExplanationThe formula for the number of subsets is 2^n. 2^4 = 16. Tip: This includes the empty set and the set itself.
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Question 22 of 100
In a group, 46 people like tea, 22 like coffee, and 7 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 46 + 22 - 7 = 61. Tip: Subtract the intersection so it isn't counted twice.
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Question 23 of 100
In a group, 28 people like tea, 46 like coffee, and 15 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 28 + 46 - 15 = 59. Tip: Subtract the intersection so it isn't counted twice.
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Question 24 of 100
In a group, 40 people like tea, 50 like coffee, and 9 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 40 + 50 - 9 = 81. Tip: Subtract the intersection so it isn't counted twice.
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Question 25 of 100
In a class of 79 students, 57 play cricket and 32 play football. If every student plays at least one game, how many play both?
Explanationn(A ∩ B) = n(A) + n(B) - n(A ∪ B) = 57 + 32 - 79 = 10. Tip: Both = (Sum of individual) - Total.
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Question 26 of 100
In a group, 29 people like tea, 41 like coffee, and 7 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 29 + 41 - 7 = 63. Tip: Subtract the intersection so it isn't counted twice.
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Question 27 of 100
In a group, 43 people like tea, 37 like coffee, and 5 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 43 + 37 - 5 = 75. Tip: Subtract the intersection so it isn't counted twice.
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Question 28 of 100
In a group, 37 people like tea, 29 like coffee, and 20 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 37 + 29 - 20 = 46. Tip: Subtract the intersection so it isn't counted twice.
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Question 29 of 100
In a class of 56 students, 42 play cricket and 39 play football. If every student plays at least one game, how many play both?
Explanationn(A ∩ B) = n(A) + n(B) - n(A ∪ B) = 42 + 39 - 56 = 25. Tip: Both = (Sum of individual) - Total.
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Question 30 of 100
In a group, 43 people like tea, 21 like coffee, and 13 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 43 + 21 - 13 = 51. Tip: Subtract the intersection so it isn't counted twice.
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Question 31 of 100
In a group, 35 people like tea, 49 like coffee, and 24 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 35 + 49 - 24 = 60. Tip: Subtract the intersection so it isn't counted twice.
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Question 32 of 100
If a set contains 5 elements, how many subsets does it have?
ExplanationThe formula for the number of subsets is 2^n. 2^5 = 32. Tip: This includes the empty set and the set itself.
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Question 33 of 100
In a group, 37 people like tea, 32 like coffee, and 30 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 37 + 32 - 30 = 39. Tip: Subtract the intersection so it isn't counted twice.
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Question 34 of 100
In a class of 69 students, 57 play cricket and 48 play football. If every student plays at least one game, how many play both?
Explanationn(A ∩ B) = n(A) + n(B) - n(A ∪ B) = 57 + 48 - 69 = 36. Tip: Both = (Sum of individual) - Total.
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Question 35 of 100
In a class of 80 students, 55 play cricket and 41 play football. If every student plays at least one game, how many play both?
Explanationn(A ∩ B) = n(A) + n(B) - n(A ∪ B) = 55 + 41 - 80 = 16. Tip: Both = (Sum of individual) - Total.
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Question 36 of 100
If a set contains 7 elements, how many subsets does it have?
ExplanationThe formula for the number of subsets is 2^n. 2^7 = 128. Tip: This includes the empty set and the set itself.
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Question 37 of 100
In a class of 85 students, 56 play cricket and 47 play football. If every student plays at least one game, how many play both?
Explanationn(A ∩ B) = n(A) + n(B) - n(A ∪ B) = 56 + 47 - 85 = 18. Tip: Both = (Sum of individual) - Total.
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Question 38 of 100
In a group, 41 people like tea, 47 like coffee, and 11 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 41 + 47 - 11 = 77. Tip: Subtract the intersection so it isn't counted twice.
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Question 39 of 100
In a class of 77 students, 44 play cricket and 35 play football. If every student plays at least one game, how many play both?
Explanationn(A ∩ B) = n(A) + n(B) - n(A ∪ B) = 44 + 35 - 77 = 2. Tip: Both = (Sum of individual) - Total.
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Question 40 of 100
In a group, 45 people like tea, 26 like coffee, and 6 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 45 + 26 - 6 = 65. Tip: Subtract the intersection so it isn't counted twice.
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Question 41 of 100
In a class of 70 students, 40 play cricket and 48 play football. If every student plays at least one game, how many play both?
Explanationn(A ∩ B) = n(A) + n(B) - n(A ∪ B) = 40 + 48 - 70 = 18. Tip: Both = (Sum of individual) - Total.
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Question 42 of 100
If a set contains 3 elements, how many subsets does it have?
ExplanationThe formula for the number of subsets is 2^n. 2^3 = 8. Tip: This includes the empty set and the set itself.
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Question 43 of 100
In a group, 28 people like tea, 47 like coffee, and 7 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 28 + 47 - 7 = 68. Tip: Subtract the intersection so it isn't counted twice.
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Question 44 of 100
In a group, 37 people like tea, 31 like coffee, and 10 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 37 + 31 - 10 = 58. Tip: Subtract the intersection so it isn't counted twice.
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Question 45 of 100
In a group, 48 people like tea, 41 like coffee, and 20 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 48 + 41 - 20 = 69. Tip: Subtract the intersection so it isn't counted twice.
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Question 46 of 100
In a class of 83 students, 37 play cricket and 47 play football. If every student plays at least one game, how many play both?
Explanationn(A ∩ B) = n(A) + n(B) - n(A ∪ B) = 37 + 47 - 83 = 1. Tip: Both = (Sum of individual) - Total.
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Question 47 of 100
In a group, 38 people like tea, 49 like coffee, and 18 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 38 + 49 - 18 = 69. Tip: Subtract the intersection so it isn't counted twice.
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Question 48 of 100
In a group, 29 people like tea, 38 like coffee, and 10 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 29 + 38 - 10 = 57. Tip: Subtract the intersection so it isn't counted twice.
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Question 49 of 100
If a set contains 7 elements, how many proper subsets does it have?
ExplanationProper subsets formula is (2^n) - 1. (2^7) - 1 = 127. Tip: The set itself is not a proper subset, so subtract 1.
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Question 50 of 100
In a class of 59 students, 51 play cricket and 45 play football. If every student plays at least one game, how many play both?
Explanationn(A ∩ B) = n(A) + n(B) - n(A ∪ B) = 51 + 45 - 59 = 37. Tip: Both = (Sum of individual) - Total.
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Question 51 of 100
In a group, 25 people like tea, 26 like coffee, and 9 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 25 + 26 - 9 = 42. Tip: Subtract the intersection so it isn't counted twice.
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Question 52 of 100
In a class of 63 students, 39 play cricket and 33 play football. If every student plays at least one game, how many play both?
Explanationn(A ∩ B) = n(A) + n(B) - n(A ∪ B) = 39 + 33 - 63 = 9. Tip: Both = (Sum of individual) - Total.
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Question 53 of 100
If a set contains 4 elements, how many proper subsets does it have?
ExplanationProper subsets formula is (2^n) - 1. (2^4) - 1 = 15. Tip: The set itself is not a proper subset, so subtract 1.
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Question 54 of 100
In a class of 76 students, 56 play cricket and 55 play football. If every student plays at least one game, how many play both?
Explanationn(A ∩ B) = n(A) + n(B) - n(A ∪ B) = 56 + 55 - 76 = 35. Tip: Both = (Sum of individual) - Total.
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Question 55 of 100
In a class of 76 students, 51 play cricket and 45 play football. If every student plays at least one game, how many play both?
Explanationn(A ∩ B) = n(A) + n(B) - n(A ∪ B) = 51 + 45 - 76 = 20. Tip: Both = (Sum of individual) - Total.
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Question 56 of 100
In a class of 77 students, 58 play cricket and 37 play football. If every student plays at least one game, how many play both?
Explanationn(A ∩ B) = n(A) + n(B) - n(A ∪ B) = 58 + 37 - 77 = 18. Tip: Both = (Sum of individual) - Total.
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Question 57 of 100
In a class of 96 students, 52 play cricket and 53 play football. If every student plays at least one game, how many play both?
Explanationn(A ∩ B) = n(A) + n(B) - n(A ∪ B) = 52 + 53 - 96 = 9. Tip: Both = (Sum of individual) - Total.
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Question 58 of 100
In a class of 103 students, 53 play cricket and 57 play football. If every student plays at least one game, how many play both?
Explanationn(A ∩ B) = n(A) + n(B) - n(A ∪ B) = 53 + 57 - 103 = 7. Tip: Both = (Sum of individual) - Total.
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Question 59 of 100
In a group, 48 people like tea, 39 like coffee, and 11 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 48 + 39 - 11 = 76. Tip: Subtract the intersection so it isn't counted twice.
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Question 60 of 100
In a class of 77 students, 58 play cricket and 43 play football. If every student plays at least one game, how many play both?
Explanationn(A ∩ B) = n(A) + n(B) - n(A ∪ B) = 58 + 43 - 77 = 24. Tip: Both = (Sum of individual) - Total.
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Question 61 of 100
In a group, 20 people like tea, 47 like coffee, and 11 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 20 + 47 - 11 = 56. Tip: Subtract the intersection so it isn't counted twice.
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Question 62 of 100
In a class of 101 students, 48 play cricket and 55 play football. If every student plays at least one game, how many play both?
Explanationn(A ∩ B) = n(A) + n(B) - n(A ∪ B) = 48 + 55 - 101 = 2. Tip: Both = (Sum of individual) - Total.
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Question 63 of 100
In a group, 31 people like tea, 42 like coffee, and 26 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 31 + 42 - 26 = 47. Tip: Subtract the intersection so it isn't counted twice.
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Question 64 of 100
In a class of 56 students, 54 play cricket and 35 play football. If every student plays at least one game, how many play both?
Explanationn(A ∩ B) = n(A) + n(B) - n(A ∪ B) = 54 + 35 - 56 = 33. Tip: Both = (Sum of individual) - Total.
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Question 65 of 100
In a class of 43 students, 39 play cricket and 42 play football. If every student plays at least one game, how many play both?
Explanationn(A ∩ B) = n(A) + n(B) - n(A ∪ B) = 39 + 42 - 43 = 38. Tip: Both = (Sum of individual) - Total.
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Question 66 of 100
In a class of 80 students, 60 play cricket and 46 play football. If every student plays at least one game, how many play both?
Explanationn(A ∩ B) = n(A) + n(B) - n(A ∪ B) = 60 + 46 - 80 = 26. Tip: Both = (Sum of individual) - Total.
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Question 67 of 100
In a group, 25 people like tea, 30 like coffee, and 10 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 25 + 30 - 10 = 45. Tip: Subtract the intersection so it isn't counted twice.
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Question 68 of 100
In a group, 32 people like tea, 23 like coffee, and 22 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 32 + 23 - 22 = 33. Tip: Subtract the intersection so it isn't counted twice.
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Question 69 of 100
In a class of 91 students, 43 play cricket and 49 play football. If every student plays at least one game, how many play both?
Explanationn(A ∩ B) = n(A) + n(B) - n(A ∪ B) = 43 + 49 - 91 = 1. Tip: Both = (Sum of individual) - Total.
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Question 70 of 100
In a group, 32 people like tea, 22 like coffee, and 7 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 32 + 22 - 7 = 47. Tip: Subtract the intersection so it isn't counted twice.
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Question 71 of 100
In a group, 49 people like tea, 30 like coffee, and 14 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 49 + 30 - 14 = 65. Tip: Subtract the intersection so it isn't counted twice.
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Question 72 of 100
In a group, 42 people like tea, 37 like coffee, and 33 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 42 + 37 - 33 = 46. Tip: Subtract the intersection so it isn't counted twice.
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Question 73 of 100
In a group, 27 people like tea, 32 like coffee, and 10 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 27 + 32 - 10 = 49. Tip: Subtract the intersection so it isn't counted twice.
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Question 74 of 100
If a set contains 6 elements, how many subsets does it have?
ExplanationThe formula for the number of subsets is 2^n. 2^6 = 64. Tip: This includes the empty set and the set itself.
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Question 75 of 100
In a group, 32 people like tea, 38 like coffee, and 26 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 32 + 38 - 26 = 44. Tip: Subtract the intersection so it isn't counted twice.
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Question 76 of 100
In a group, 42 people like tea, 34 like coffee, and 26 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 42 + 34 - 26 = 50. Tip: Subtract the intersection so it isn't counted twice.
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Question 77 of 100
In a class of 79 students, 56 play cricket and 53 play football. If every student plays at least one game, how many play both?
Explanationn(A ∩ B) = n(A) + n(B) - n(A ∪ B) = 56 + 53 - 79 = 30. Tip: Both = (Sum of individual) - Total.
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Question 78 of 100
In a group, 30 people like tea, 48 like coffee, and 21 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 30 + 48 - 21 = 57. Tip: Subtract the intersection so it isn't counted twice.
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Question 79 of 100
In a group, 22 people like tea, 43 like coffee, and 13 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 22 + 43 - 13 = 52. Tip: Subtract the intersection so it isn't counted twice.
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Question 80 of 100
In a class of 90 students, 57 play cricket and 51 play football. If every student plays at least one game, how many play both?
Explanationn(A ∩ B) = n(A) + n(B) - n(A ∪ B) = 57 + 51 - 90 = 18. Tip: Both = (Sum of individual) - Total.
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Question 81 of 100
In a class of 55 students, 44 play cricket and 40 play football. If every student plays at least one game, how many play both?
Explanationn(A ∩ B) = n(A) + n(B) - n(A ∪ B) = 44 + 40 - 55 = 29. Tip: Both = (Sum of individual) - Total.
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Question 82 of 100
In a group, 30 people like tea, 24 like coffee, and 20 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 30 + 24 - 20 = 34. Tip: Subtract the intersection so it isn't counted twice.
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Question 83 of 100
If a set contains 5 elements, how many proper subsets does it have?
ExplanationProper subsets formula is (2^n) - 1. (2^5) - 1 = 31. Tip: The set itself is not a proper subset, so subtract 1.
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Question 84 of 100
In a group, 27 people like tea, 43 like coffee, and 23 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 27 + 43 - 23 = 47. Tip: Subtract the intersection so it isn't counted twice.
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Question 85 of 100
In a group, 20 people like tea, 40 like coffee, and 18 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 20 + 40 - 18 = 42. Tip: Subtract the intersection so it isn't counted twice.
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Question 86 of 100
In a class of 73 students, 40 play cricket and 48 play football. If every student plays at least one game, how many play both?
Explanationn(A ∩ B) = n(A) + n(B) - n(A ∪ B) = 40 + 48 - 73 = 15. Tip: Both = (Sum of individual) - Total.
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Question 87 of 100
In a group, 35 people like tea, 36 like coffee, and 34 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 35 + 36 - 34 = 37. Tip: Subtract the intersection so it isn't counted twice.
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Question 88 of 100
If a set contains 6 elements, how many proper subsets does it have?
ExplanationProper subsets formula is (2^n) - 1. (2^6) - 1 = 63. Tip: The set itself is not a proper subset, so subtract 1.
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Question 89 of 100
In a group, 42 people like tea, 31 like coffee, and 8 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 42 + 31 - 8 = 65. Tip: Subtract the intersection so it isn't counted twice.
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Question 90 of 100
In a group, 49 people like tea, 20 like coffee, and 11 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 49 + 20 - 11 = 58. Tip: Subtract the intersection so it isn't counted twice.
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Question 91 of 100
In a group, 37 people like tea, 27 like coffee, and 12 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 37 + 27 - 12 = 52. Tip: Subtract the intersection so it isn't counted twice.
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Question 92 of 100
In a class of 57 students, 46 play cricket and 55 play football. If every student plays at least one game, how many play both?
Explanationn(A ∩ B) = n(A) + n(B) - n(A ∪ B) = 46 + 55 - 57 = 44. Tip: Both = (Sum of individual) - Total.
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Question 93 of 100
In a group, 46 people like tea, 49 like coffee, and 25 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 46 + 49 - 25 = 70. Tip: Subtract the intersection so it isn't counted twice.
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Question 94 of 100
If a set contains 8 elements, how many subsets does it have?
ExplanationThe formula for the number of subsets is 2^n. 2^8 = 256. Tip: This includes the empty set and the set itself.
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Question 95 of 100
In a class of 68 students, 41 play cricket and 47 play football. If every student plays at least one game, how many play both?
Explanationn(A ∩ B) = n(A) + n(B) - n(A ∪ B) = 41 + 47 - 68 = 20. Tip: Both = (Sum of individual) - Total.
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Question 96 of 100
In a class of 72 students, 49 play cricket and 45 play football. If every student plays at least one game, how many play both?
Explanationn(A ∩ B) = n(A) + n(B) - n(A ∪ B) = 49 + 45 - 72 = 22. Tip: Both = (Sum of individual) - Total.
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Question 97 of 100
In a group, 23 people like tea, 26 like coffee, and 13 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 23 + 26 - 13 = 36. Tip: Subtract the intersection so it isn't counted twice.
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Question 98 of 100
In a class of 45 students, 43 play cricket and 37 play football. If every student plays at least one game, how many play both?
Explanationn(A ∩ B) = n(A) + n(B) - n(A ∪ B) = 43 + 37 - 45 = 35. Tip: Both = (Sum of individual) - Total.
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Question 99 of 100
In a group, 29 people like tea, 23 like coffee, and 17 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 29 + 23 - 17 = 35. Tip: Subtract the intersection so it isn't counted twice.
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Question 100 of 100
In a group, 25 people like tea, 28 like coffee, and 16 like both. How many people like at least one of the two beverages?
ExplanationFormula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 25 + 28 - 16 = 37. Tip: Subtract the intersection so it isn't counted twice.
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