Mathematics
Venn Diagrams
Practice questions
If n(A) = 56, n(B) = 61, n(A − B) = 19, and n(B − A) = 24, what is n(A ∩ B)?If n(A) = 64, n(B) = 59, n(A − B) = 22, and n(B − A) = 20, what is the correct conclusion about the data?In a survey, n(U) = 260, n(A) = 118, n(B) = 104, n(C) = 92, n(A ∩ B) = 48, n(B ∩ C) = 41, n(C ∩ A) = 37, and n(A ∩ B ∩ C) = 16. How many are in none of the sets?In three sets, n(A∪B∪C)=172. The numbers of elements only in A, only in B, only in C, only in A∩B, only in B∩C, and only in C∩A are 38, 34, 29, 21, 18, and 16, respectively. What is n(A∩B∩C)?If, in three sets, 84 elements are in exactly one set, 63 elements are in exactly two sets, and 18 elements are in all three sets, what is n(A∪B∪C)?If n(A∪B∪C)=156, 74 elements are in exactly one set, and 17 elements are in all three sets, how many elements are in exactly two sets?In a survey, n(A)=96, n(B)=88, n(C)=82, 69 people are in exactly two sets, and 21 are in all three sets. How many people are in exactly one set?If n(A ∪ B) = 128, n(A ∩ B) = 32, and n(A − B) = 45, what is n(B)?If n(A)=102, n(B)=95, n(A∪B)=143, and n(U)=190, what is n(Aᶜ∩Bᶜ)?If n(A∩Bᶜ)=41, n(Aᶜ∩B)=34, n(A∩B)=26, and n(U)=130, what is n(Aᶜ∩Bᶜ)?If n(A ∩ Bᶜ) = 52, n(Aᶜ ∩ B) = 39, and n(A △ B) = 100, what is the correct conclusion about the data?For three sets A, B, and C, n(A) = 84, n(B) = 78, and n(C) = 72. There are 96 elements in exactly one set and 12 elements in all three sets. How many elements are in exactly two sets?If n(A ∪ B ∪ C) = 205, n(A ∩ B ∩ C) = 24, and exactly two sets contain a total of 83 elements, how many elements are in exactly one set?If n(A − B) = x, n(B − A) = 3x, n(A ∩ B) = 24, and n(A ∪ B) = 120, what is x?In a Venn diagram, n(A) = 91, n(B) = 87, and n(A ∩ B) = 34. If n(U) = 190, what is n((A ∪ B)ᶜ)?If n(A △ B) = 112 and n(A ∩ B) = 39, what is n(A ∪ B)?For three sets, n(A) = 90, n(B) = 84, n(C) = 78, n(A ∩ B) = 36, n(B ∩ C) = 32, n(C ∩ A) = 30, and n(A ∩ B ∩ C) = 13. What is n(A ∪ B ∪ C)?If n(U) = 180, n(A) = 105, and n(B) = 96, what is the minimum possible value of n(A ∩ B)?If n(A ∪ B) = 136, n(A − B) = 49, and n(A ∩ B) = 31, what is n(B)?Let U = {1, 2, 3, ..., 96}, A be the numbers divisible by 4, and B be the numbers divisible by 6. What is n(A ∪ B)?