Mathematics
Venn Diagrams
Practice questions
In a two-set Venn diagram, n(A−B)=18, n(A∩B)=14, n(B−A)=21, and 7 elements are outside both sets. What is n(U)?If n(U) = 88, n(A − B) = 24, n(A ∩ B) = 13, and n(B − A) = 26, what is the number of elements in the outside region of the Venn diagram?In a Venn diagram, n(A ∪ B) = 86 and n(A ∩ B) = 31. How many elements belong to exactly one of the two sets?For three sets, n(A)=35, n(B)=32, n(C)=29, n(A∩B)=12, n(B∩C)=10, n(C∩A)=9, and n(A∩B∩C)=4. What is n(A∪B∪C)?For three sets, n(A∩B)=18, n(B∩C)=16, n(C∩A)=14, and n(A∩B∩C)=6. How many elements belong to exactly two of the sets?If n(A)=50, n(A∩B)=21, n(A∩C)=19, and n(A∩B∩C)=8, how many elements are only in A, that is, in A but not in B or C?If n(A∩B)=24 and n(A∩B∩C)=9, how many elements are only in A and B but not in C?Which part does A△B show in a Venn diagram?If n(A △ B) = 64 and n(A − B) = 27, what is n(B − A)?If n(A) = 39, n(B) = 44, and 51 elements lie in exactly one of the two sets, what is n(A ∩ B)?Among 72 students, 34 like Mathematics, 31 like Physics, and 13 like both subjects. How many like neither subject?In a group, 45 people like tea, 36 like coffee, and 15 like both. How many like only tea?If A is a subset of B, what is A union B equal to in a Venn diagram?If n(A) = 36, n(B) = 42, and A intersection B is the empty set, how many elements are in exactly one set?If n(A union B) = 70, n(A − B) = 26, and n(B − A) = 19, what is n(A intersection B)?If n(U) = 100, n(A) = 48, n(B) = 46, and n((A union B) complement) = 18, what is n(A intersection B)?In three sets, n(A ∩ B ∩ C) = 11. Which part of the Venn diagram does this represent?If only A = 14, only B = 18, only C = 16, only A ∩ B = 7, only B ∩ C = 6, only C ∩ A = 5, and A ∩ B ∩ C = 4, what is n(A ∪ B ∪ C)?In three sets, only A = 20, only A ∩ B = 8, only C ∩ A = 6, and A ∩ B ∩ C = 5. What is n(A)?In a three-set Venn diagram, only B = 17, only A ∩ B = 9, only B ∩ C = 11, and A ∩ B ∩ C = 6. What is n(B)?