Mathematics
Venn Diagrams
Practice questions
If n(A) = 35, n(B) = 30, and n(A ∪ B) = 50, what is n(A ∩ B) in the Venn diagram?In a survey, n(U) = 80, n(A) = 45, n(B) = 37, and n(A ∩ B) = 18. How many students are in neither group?If n(A) = 32 and n(A ∩ B) = 14, how many elements are only in A in the Venn diagram?If n(B) = 41 and n(A ∩ B) = 17, how many elements are in the region that belongs only to B?In a Venn diagram of two sets, n(A − B) = 12, n(B − A) = 9, and n(A ∩ B) = 6. What is n(A ∪ B)?If A ⊆ B, n(A) = 18, and n(B) = 45, what is n(B − A)?If A ∩ B = ∅, n(A) = 26, and n(B) = 19, what is n(A ∪ B)?Which part does A ∩ B show in a Venn diagram?In a group, 40 people like tea, 32 like coffee, and 18 like both. How many like at least one drink?In a survey, 27 students study Mathematics, 34 study Science, and 12 study both. How many study only Mathematics?If n(A ∪ B) = 48, n(A − B) = 20, and n(B − A) = 13, what is n(A ∩ B)?For three sets, which part is A ∩ B ∩ C in a Venn diagram?If n(A)=30, n(B)=28, n(C)=24, n(A ∩ B)=10, n(B ∩ C)=8, n(C ∩ A)=6, and n(A ∩ B ∩ C)=4, what is n(A ∪ B ∪ C)?In three sets, how do we find the number of elements in only A?If n(A)=42, n(A ∩ B)=15, n(A ∩ C)=18, and n(A ∩ B ∩ C)=7, how many elements are only in A?If n(A ∩ B)=14 and n(A ∩ B ∩ C)=5, how many elements are in A and B but not in C?If n(U)=90 and n(A ∪ B ∪ C)=76, how many elements are in none of the sets?If A and B are two overlapping circles in a Venn diagram, which part is A − B?What region does A △ B represent in a Venn diagram?If n(A−B)=23 and n(B−A)=31, what is n(A △ B)?