If n(U) = 70, the outside region has 12 elements, only A has 18 elements, and only B has 20 elements, what is n(A ∩ B)?
Answer and explanation
Correct answer: 20
The universal set is partitioned into four disjoint Venn-diagram regions: outside both sets, only A, A ∩ B, and only B. Their cardinalities must add to n(U). Thus, 12 + 18 + n(A ∩ B) + 20 = 70. The known regions total 50, so n(A ∩ B) = 70 − 50 = 20. Therefore, option A is correct; the other values result from incomplete or incorrect addition and subtraction.
Frequently asked questions
What is the correct answer to this question?
20
Why is this the correct answer?
The universal set is partitioned into four disjoint Venn-diagram regions: outside both sets, only A, A ∩ B, and only B. Their cardinalities must add to n(U). Thus, 12 + 18 + n(A ∩ B) + 20 = 70. The known regions total 50, so n(A ∩ B) = 70 − 50 = 20. Therefore, option A is correct; the other values result from incomplete or incorrect addition and subtraction.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
