Mathematics
Venn Diagrams
Practice questions
Let U={1,2,...,60}, A be the set of multiples of 3, and B be the set of multiples of 4. What is n((A∪B)′)?In a survey, n(U)=210, n(A)=96, n(B)=88, n(C)=74, n(A∩B)=39, n(B∩C)=31, n(C∩A)=28, and n(A∩B∩C)=14. How many people are in none of the sets?If n(A)=78, n(B)=69, n(C)=63, n(A∩B)=30, n(B∩C)=25, n(C∩A)=21, and n(A∩B∩C)=9, how many elements are only in set A?In a Venn diagram, only A has 18 elements, only B has 22, only C has 16, only A∩B has 11, only B∩C has 13, only C∩A has 9, and all three have 6 elements. How many elements are in at least two sets?If n(A∪B)=112, n(A−B)=43, and n(B−A)=37, what is n(A∩B)?If n(U)=140, n(A′)=58, n(B′)=71, and n(A∩B)=34, what is n(A∪B)?If n(A∩B′)=29, n(A′∩B)=33, n(A∩B)=17, and n((A∪B)′)=21, what is n(U)?In three clubs, n(A) = 72, n(B) = 68, n(C) = 61, n(A ∩ B) = 29, n(B ∩ C) = 24, n(C ∩ A) = 26, and n(A ∩ B ∩ C) = 11. How many members are only in B?If n(A ∪ B ∪ C) = 135, exactly one set contains 58 elements, and exactly two sets contain 49 elements, what is n(A ∩ B ∩ C)?If U = {1, 2, ..., 84}, A is the set of multiples of 7 and B is the set of multiples of 4, what is n((A ∪ B)')?If A = {x ∈ N : x ≤ 20}, B = {x : x is odd and x ≤ 20}, and C = {x : x is a multiple of 5 and x ≤ 20}, what is n(B ∩ C)?Which region does A − (B ∩ C) represent in a Venn diagram?If (A\cap B=A) and (A\neq \varnothing), which relation is correct?If only (A\cap B) has (14), only (B\cap C) has (12), only (C\cap A) has (15), and (A\cap B\cap C) has (8) elements, then what is (n((A\cap B)\cup(B\cap C)\cup(C\cap A)))?If only A has 31 elements, only B has 27 elements, only C has 25 elements, the total of the exactly-two-set regions is 42, and all three sets have 11 elements, then what is n(A ∪ B ∪ C)?Suppose n(A)=70, n(B)=65, n(C)=60, n(A ∪ B ∪ C)=128, n(A ∩ B)=27, n(B ∩ C)=24, and n(C ∩ A)=22. Which conclusion is mathematically correct?If n(A ∩ (B ∪ C)) = 44, only (A ∩ B) contains 18 elements and only (A ∩ C) contains 16 elements, then what is n(A ∩ B ∩ C)?Which statement correctly describes the Venn region represented by A ∩ (B − C)?If A, B and C are mutually disjoint, n(A) = 18, n(B) = 24, n(C) = 29 and n(U) = 90, then what is n((A ∪ B ∪ C)')?If A ⊆ B ⊆ C, then what is A ∪ B ∪ C equal to?