Mathematics
Venn Diagrams
Practice questions
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)?If n(A ∩ Bᶜ) = 48, n(Aᶜ ∩ B) = 44, n(A ∩ B) = 28, and n(U) = 160, what is n(Aᶜ ∩ Bᶜ)?If n(A ∪ B) = 96, n(A) = 58, and n(B) = 49, find n(A ∩ B).In a class, n(U) = 90, n(A) = 52, n(B) = 47, and n(A ∩ B) = 24. How many students are in neither A nor B?If n(U) = 150 and n(A ∪ B) = 118, what is the number of elements in (A ∪ B)ᶜ?For three sets, n(A) = 40, n(B) = 38, n(C) = 35, n(A ∩ B) = 14, n(B ∩ C) = 12, n(C ∩ A) = 10, and n(A ∩ B ∩ C) = 5. What is n(A ∪ B ∪ C)?In a Venn diagram, n(A∩B∩C)=7, only A∩B is 9, only B∩C is 6, only C∩A is 5, and only A is 18. What is n(A)?In a survey, the universal set U has 200 people, and 164 people belong to at least one of the sets A, B, or C. How many people belong to none of the three sets?If only A, only B, only C, exactly two sets, and all three sets contain 16, 19, 14, 27, and 8 elements respectively, how many elements are in at least one set?In a group of 80 students, 46 chose Mathematics, 39 chose Physics, and 22 chose both. How many students chose only Physics?If A is a subset of B, n(A) = 28, and n(B) = 64, how many elements are in the region B − A of the Venn diagram?If A∩B=∅, n(A)=31, and n(B)=44, what is n(A∪B)?If n(A−B)=23, n(B−A)=17, and n(A∩B)=12, what is n(A∪B)?In a Venn diagram, why must expressions such as n(A−B)=18, n(B−C)=26, and n(C−A)=21 be handled carefully?In a Venn diagram, n(A ∪ B) = 70, n(A − B) = 24, and n(B − A) = 31. What is n(A ∩ B)?Which formula correctly gives the number of elements belonging to exactly two of three sets?If n(A ∩ B)=20, n(B ∩ C)=18, n(C ∩ A)=16, and n(A ∩ B ∩ C)=6, how many elements are in exactly two sets?In a survey there are 45 people in set A, 50 in B, and 42 in C; n(A ∩ B)=18, n(B ∩ C)=20, n(C ∩ A)=16, and 7 people are in all three. How many people are only in A?