If n(A) = 3x + 2, n(B) = 2x + 5, n(A ∩ B) = x + 1, and n(A ∪ B) = 30, what is the value of x?
Advertisement
Answer and explanation
Correct answer: 6
For two finite sets, n(A ∪ B) = n(A) + n(B) − n(A ∩ B), because the common elements are counted twice when n(A) and n(B) are added. Substituting the given expressions gives 30 = (3x + 2) + (2x + 5) − (x + 1) = 4x + 6. Therefore, 4x = 24 and x = 6. Hence, option A is correct.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
For two finite sets, n(A ∪ B) = n(A) + n(B) − n(A ∩ B), because the common elements are counted twice when n(A) and n(B) are added. Substituting the given expressions gives 30 = (3x + 2) + (2x + 5) − (x + 1) = 4x + 6. Therefore, 4x = 24 and x = 6. Hence, option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
Advertisement