Mathematics
Venn Diagrams
Practice questions
If U = {1, 2, 3, ..., 64}, A is the set of square numbers in U, and B is the set of even numbers in U, then what is n(A ∩ B)?Which region does ((A ∪ B)' ∩ C) represent in a Venn diagram?In a Venn diagram, A − (B ∪ C) is equal to what?If A ⊆ B, how is the statement B' ⊆ A' according to the Venn diagram?If A ∩ B = A and B ∩ C = B, then what is A ∩ C equal to?If A ∩ B = ∅, then (A ∪ B) − A is equal to what?If n(A ∪ B) = n(B), which relation is correct according to the Venn diagram?If n(A ∩ B) = 0, n(A) = 39, and n(B) = 48, what is n(A △ B)?In a library, among 150 students, 83 read novels, 69 read poetry, and 28 read neither. How many read both?In an exam, among 180 students, 97 solved A, 88 solved B, 82 solved C, 41 solved A and B, 36 solved B and C, 34 solved C and A, and 18 solved all three. How many solved at least one question?If only A∩B has 19 elements, only B∩C has 17 elements, only C∩A has 21 elements, and A∩B∩C has 11 elements, how many elements are in at least two sets?If n(A)=82, n(B)=77, n(C)=69, n(A∪B∪C)=151, n(A∩B)=32, n(B∩C)=28, and n(C∩A)=25, what is n(A∩B∩C)?If n(A∩(B∪C))=52, only A∩B has 23 elements and only A∩C has 18 elements, what is n(A∩B∩C)?If n(A−B)=0, n(B−C)=0 and n(A)>0, which relation must be true?If n(A∪B∪C)=184, n(A)=86, n(B)=91, n(C)=88 and n(A∩B∩C)=23, what is n(A∩B)+n(B∩C)+n(C∩A)?If only n(A−B)=24, n(B−C)=27 and n(C−A)=22 are given, can n(A∪B∪C) be determined uniquely?Assertion: If A ⊆ B, then A ∩ B = A. Reason: Every element of A is also in B. Choose the correct option.In a Venn diagram, n(A ∪ B ∪ C) = 215 and n((A ∪ B ∪ C)′) = 35. Exactly two sets have 62 elements. If n(U) is asked, what is the answer?If n(A) = 92, n(B) = 85, n(C) = 78, n(A ∩ B) = 37, n(B ∩ C) = 34, n(C ∩ A) = 29, and n(A ∩ B ∩ C) = 16, how many elements are only in B ∩ C?If U = {1, 2, ..., 180}, A is the set of multiples of 12, B is the set of multiples of 15, and C is the set of multiples of 20, what is n((A ∪ B ∪ C)′)?