If \(n(A)=30\), \(n(B)=24\), and \(n(A\setminus B)=18\), what is the value of \(n(A\cup B)\)?
Answer and explanation
Correct answer: 42
The set \(A\setminus B\) consists of elements in A but not in B. Therefore, the elements common to A and B number \(n(A\cap B)=n(A)-n(A\setminus B)=30-18=12\). Applying the inclusion-exclusion formula gives \(n(A\cup B)=n(A)+n(B)-n(A\cap B)=30+24-12=42\). We subtract the intersection once because those 12 elements were counted in both 30 and 24.
Frequently asked questions
What is the correct answer to this question?
42
Why is this the correct answer?
The set \(A\setminus B\) consists of elements in A but not in B. Therefore, the elements common to A and B number \(n(A\cap B)=n(A)-n(A\setminus B)=30-18=12\). Applying the inclusion-exclusion formula gives \(n(A\cup B)=n(A)+n(B)-n(A\cap B)=30+24-12=42\). We subtract the intersection once because those 12 elements were counted in both 30 and 24.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
