Mathematics
Venn Diagrams
Practice questions
Given n(U)=140, n(A)=60, n(B)=55, n(C)=50, n(A∩B)=24, n(B∩C)=21, n(C∩A)=19, and n(A∩B∩C)=8, how many elements are in none of the sets?If n(A)=40, n(B)=36, n(C)=34, n(A∪B∪C)=82, n(A∩B)=12, n(B∩C)=10, and n(C∩A)=9, what is n(A∩B∩C)?In a Venn diagram, what is (A − B) ∪ (A ∩ B) equal to?In a Venn diagram, what is ((A ∪ B) − A) equal to?If n(A∪B)=58, n(A−B)=22, and n(B−A)=20, which statement is correct?In a Venn diagram, n(U) = 85, n(A) = 42, n(B) = 36, and n(A ∩ B) = 14. How many elements are in neither set?If n(A ∪ B) = 74, n(A − B) = 28, and n(B − A) = 19, what is n(A ∩ B)?For three sets, n(A) = 38, n(A ∩ B) = 16, n(A ∩ C) = 13, and n(A ∩ B ∩ C) = 5. How many elements belong only to A?In a Venn diagram, n(U) = 110, n(A) = 57, n(B) = 49, and n(A ∩ B) = 21. What is n(A ∪ B)?In a survey, n(U) = 140, n(A) = 72, n(B) = 64, and n(A ∩ B) = 28. How many people are in neither set?If n(A) = 59 and n(A ∩ B) = 24, how many elements are only in A, that is, in A but not in B?In a two-set Venn diagram, n(A − B) = 26, n(A ∩ B) = 18, n(B − A) = 33, and 12 elements are outside both sets. What is n(U)?If n(U)=96, n(A−B)=29, n(A∩B)=17, and n(B−A)=22, what is the number of elements outside A∪B in the Venn diagram?If A⊆B, n(A)=34, and n(B)=82, what is n(B−A)?If A∩B=∅, n(A)=45, and n(B)=37, what is n(A∪B)?In a Venn diagram, n(A∪B)=98 and n(A∩B)=42. How many elements belong to exactly one of the two sets?For three sets, n(A)=42, n(B)=39, n(C)=35, n(A∩B)=15, n(B∩C)=13, n(C∩A)=11, and n(A∩B∩C)=5. What is n(A∪B∪C)?For three sets A, B, C, n(A∩B)=21, n(B∩C)=19, n(C∩A)=16, and n(A∩B∩C)=7. How many elements belong to exactly two of the sets?If n(A)=63, n(A∩B)=26, n(A∩C)=24, and n(A∩B∩C)=9, how many elements are only in A?If n(A∩B)=29 and n(A∩B∩C)=12, how many elements are only in A and B but not in C?