If \(n(A)=5\), \(n(B)=4\), and \(n(A\cap B)=2\), what is \(n(A\cup B)\)?
Advertisement
Answer and explanation
Correct answer: 7
For two finite sets, the cardinality of the union is found using \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\). Substituting the given values gives \(5+4-2=7\). We subtract 2 because the common elements would otherwise be counted once in A and again in B. Therefore, option A, 7, is correct.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
For two finite sets, the cardinality of the union is found using \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\). Substituting the given values gives \(5+4-2=7\). We subtract 2 because the common elements would otherwise be counted once in A and again in B. Therefore, option A, 7, is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
Advertisement