Mathematics
Venn Diagrams
Practice questions
If n(A ∪ B ∪ C) = 160, n(A) = 70, n(B) = 75, n(C) = 80 and n(A ∩ B ∩ C) = 18, then what is n(A ∩ B) + n(B ∩ C) + n(C ∩ A)?Assertion: n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Reason: Elements of A ∩ B are counted twice in n(A) + n(B). Choose the correct option.Assertion: If A ∩ B = ∅, then n(A ∪ B) = n(A) + n(B). Reason: Disjoint sets have no common elements or common region. Choose the correct option.In a Venn diagram, n(A ∪ B ∪ C) = 190 and n((A ∪ B ∪ C)′) = 25. What is n(U)?If n(A ∪ B ∪ C) = 155, n(A ∪ B) = 118, n(B ∪ C) = 124, n(C ∪ A) = 121, and n(B) = 64, then what is n((A ∩ C) − B)?In a survey, n(U) = 240, n(A) = 112, n(B) = 104, n(C) = 93, n(A ∩ B) = 46, n(B ∩ C) = 38, n(C ∩ A) = 35, and n(A ∩ B ∩ C) = 17. How many elements are in none of the sets?If n(A) = 86, n(B) = 79, n(C) = 71, n(A ∩ B) = 34, n(B ∩ C) = 29, n(C ∩ A) = 27, and n(A ∩ B ∩ C) = 12, then how many elements are only in C?In a Venn diagram, only A has 26 elements, only B has 31, only C has 24, only A ∩ B has 14, only B ∩ C has 16, only C ∩ A has 12, and all three have 9 elements. How many elements are in exactly one set?If n(A ∪ B) = 126, n(A − B) = 48, and n(B − A) = 41, then what is n(A ∩ B)?If n(U) = 160, n(A′) = 63, n(B′) = 72, and n(A ∩ B) = 39, then what is n(A ∪ B)?If n(A ∩ B') = 36, n(A' ∩ B) = 44, n(A ∩ B) = 25 and n((A ∪ B)') = 18, then what is n(U)?In a class of 110 students, 68 study Biology, 57 study Chemistry, and 32 study both subjects. How many students study neither Biology nor Chemistry?If A ⊆ B, n(A) = 52, n(B) = 91 and n(U) = 140, then what is n((B − A) ∪ B')?For three activities, n(A) = 84, n(B) = 77, n(C) = 73, n(A ∩ B) = 33, n(B ∩ C) = 28, n(C ∩ A) = 31 and n(A ∩ B ∩ C) = 13. How many students are only in A ∩ C, that is, in A and C but not in B?If U = {1, 2, ..., 96}, A is the set of multiples of 6 and B is the set of multiples of 10, then what is n(A ∪ B)?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?