Mathematics
Venn Diagrams
Practice questions
If n(U) = 150, n(A) = 66, and n(B) = 59, what is the maximum possible value of n(A ∩ B)?If A ⊆ B ⊆ C, n(C) = 118, n(B) = 73, and n(A) = 29, what is n(C − A)?For three sets, n(A)=64, n(B)=58, n(C)=52, n(A∩B)=24, n(B∩C)=21, n(C∩A)=19, and n(A∩B∩C)=8. What is n(A∪B∪C)?If n(A)=70, n(B)=65, n(C)=60, n(A∪B∪C)=140, n(A∩B)=28, n(B∩C)=24, and n(C∩A)=22, what is n(A∩B∩C)?In three sets, n(A∩B)=31, n(B∩C)=29, n(C∩A)=25, and n(A∩B∩C)=12. How many elements are in exactly two sets?If n(A)=80, n(A∩B)=35, n(A∩C)=32, and n(A∩B∩C)=14, how many elements are only in A?If n(A∩B)=42, n(A∩C)=36, n(B∩C)=34, and n(A∩B∩C)=15, how many elements are in at least two sets?If only A=18, only A∩B=12, only A∩C=10, and A∩B∩C=6, what is n(A)?In a Venn diagram, n(A △ B) = 82 and n(A ∪ B) = 119. What is n(A ∩ B)?In a Venn diagram, what is (A ∪ B) − (A ∩ B) equal to?Let \(U\) be a universal set with \(n(U)=200\). If \(n(A\cup B)=128\), \(n(A\cap B)=36\), and \(n(A^c\cap B^c)=72\), which relation is true?Let U = {1, 2, 3, ..., 100}. A is the set of numbers divisible by 2, B the set of numbers divisible by 5, and C the set of numbers divisible by 10. Which relation is correct?If n(A ∪ B) = n(A) + n(B), which conclusion is correct according to the Venn diagram?If n(A ∪ B) = n(A), which relation must be true?If n(A ∩ B) = n(A), which relation must be true?If n(A) = 55, n(B) = 50, n(A − B) = 20, and n(B − A) = 18, what is the correct conclusion about the given data?In a survey, n(U) = 200, n(A) = 96, n(B) = 88, n(C) = 74, n(A ∩ B) = 40, n(B ∩ C) = 31, n(C ∩ A) = 29, and n(A ∩ B ∩ C) = 12. How many people are in none of the sets?In three sets, n(A ∪ B ∪ C) = 150. If only A = 32, only B = 28, only C = 24, only A ∩ B = 18, only B ∩ C = 16, and only C ∩ A = 14, what is n(A ∩ B ∩ C)?If in three sets there are 71 elements belonging to exactly one set, 46 elements belonging to exactly two sets, and 15 elements belonging to all three sets, what is n(A ∪ B ∪ C)?In a survey, n(A) = 82, n(B) = 76, n(C) = 70, 54 people are in exactly two sets, and 18 are in all three sets. How many people are in exactly one set?