If \(|A\cup B|=92\), \(|A\setminus B|=31\), and \(|A\cap B|=27\), what is \(|B|\)?
Advertisement
Answer and explanation
Correct answer: 61
The union is partitioned into three disjoint regions: \(A\setminus B\), \(A\cap B\), and \(B\setminus A\). Thus, \(|B\setminus A|=|A\cup B|-|A\setminus B|-|A\cap B|=92-31-27=34\). Set \(B\) consists of \(B\setminus A\) together with \(A\cap B\), so \(|B|=34+27=61\). Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
61
Why is this the correct answer?
The union is partitioned into three disjoint regions: \(A\setminus B\), \(A\cap B\), and \(B\setminus A\). Thus, \(|B\setminus A|=|A\cup B|-|A\setminus B|-|A\cap B|=92-31-27=34\). Set \(B\) consists of \(B\setminus A\) together with \(A\cap B\), so \(|B|=34+27=61\). Therefore, option A 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