Mathematics
Venn Diagrams
Practice questions
If n(A ∪ B) = 104, n(A ∩ B) = 26, and n(A − B) = 37, what is n(B)?In a Venn diagram, n(A − B) = 25, n(B − A) = 30, n(A ∩ B) = 20, and n((A ∪ B)ᶜ) = 15. What is n(Aᶜ)?In a Venn diagram, what is (A ∪ B) ∩ (A ∪ Bᶜ) equal to?For three sets A, B, and C, n(A) = 72, n(B) = 66, and n(C) = 60. Exactly one set contains 84 elements, and all three sets together contain 10 elements. How many elements belong to exactly two sets?If n(A ∪ B) = 115, n(A) = 73, n(B) = 67, and n(U) = 150, what is n(Aᶜ ∪ Bᶜ)?If n(A ∪ B ∪ C) = 180, n(A ∩ B ∩ C) = 20, and 70 elements lie in exactly two of the sets, how many elements lie in exactly one set?If n(A − B) = x, n(B − A) = 2x, n(A ∩ B) = 15, and n(A ∪ B) = 75, what is the value of x?In a Venn diagram, n(U) = 210, n(A) = 96, n(B) = 88, and n((A ∪ B)ᶜ) = 58. What is n(A ∩ B)?In a class, n(A) = 86, n(B) = 78, and the number of students in exactly one set is 98. What is n(A ∩ B)?For three sets, n(A) = 72, n(B) = 66, n(C) = 59, n(A ∩ B) = 28, n(B ∩ C) = 24, n(C ∩ A) = 22, and n(A ∩ B ∩ C) = 9. What is n(A ∪ B ∪ C)?If n(A) = 82, n(B) = 76, n(C) = 70, n(A ∪ B ∪ C) = 162, n(A ∩ B) = 34, n(B ∩ C) = 30, and n(C ∩ A) = 27, what is n(A ∩ B ∩ C)?In three sets, n(A ∩ B) = 36, n(B ∩ C) = 33, n(C ∩ A) = 31, and n(A ∩ B ∩ C) = 14. How many elements belong to exactly two sets?If n(A ∩ B) = 48, n(A ∩ C) = 41, n(B ∩ C) = 39, and n(A ∩ B ∩ C) = 17, how many elements belong to at least two sets?In three sets, only A = 31, only B = 26, only C = 24, only A ∩ B = 15, only B ∩ C = 13, only C ∩ A = 11, and A ∩ B ∩ C = 8. If n(U) = 160, what is n((A ∪ B ∪ C)ᶜ)?If only A = 25, only A ∩ B = 14, only A ∩ C = 12, and A ∩ B ∩ C = 9, what is n(A)?In a Venn diagram, n(A Δ B) = 96 and n(A ∪ B) = 137. What is n(A ∩ B)?If n(A) = 88, n(B) = 82, and n(A △ B) = 104, what is n(A ∩ B)?If n(U) = 240, n(A ∪ B) = 157, and n(Aᶜ ∩ Bᶜ) = 83, which relation is true?U = {1, 2, 3, ..., 72}, A = {x : x is divisible by 6}, and B = {x : x is divisible by 8}. What is n(A ∪ B)?U = {1, 2, 3, ..., 90}, A is the set of numbers divisible by 2, B by 3, and C by 5. What is n(A ∩ B ∩ C)?