If \(n(A\cup B)=70\), \(n(A\setminus B)=22\), and \(n(B\setminus A)=31\), then what is \(n(A\cap B)\)?
Answer and explanation
Correct answer: 17
The union \(A\cup B\) is partitioned into three mutually disjoint regions: elements belonging only to A, elements belonging only to B, and elements belonging to both sets. Thus, \(n(A\cup B)=n(A\setminus B)+n(B\setminus A)+n(A\cap B)\). Substituting the values gives \(70=22+31+n(A\cap B)\), so \(n(A\cap B)=70-53=17\).
Frequently asked questions
What is the correct answer to this question?
17
Why is this the correct answer?
The union \(A\cup B\) is partitioned into three mutually disjoint regions: elements belonging only to A, elements belonging only to B, and elements belonging to both sets. Thus, \(n(A\cup B)=n(A\setminus B)+n(B\setminus A)+n(A\cap B)\). Substituting the values gives \(70=22+31+n(A\cap B)\), so \(n(A\cap B)=70-53=17\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
