If \(A\subseteq B\), \(n(A)=15\), and \(n(B)=52\), what is \(n(A\cap B)\)?
Answer and explanation
Correct answer: 15
Because \(A\subseteq B\), every element of A is also an element of B. The elements common to A and B are therefore exactly the elements of A, so \(A\cap B=A\). It follows that \(n(A\cap B)=n(A)=15\). The value 52 is the size of B, not the intersection; 37 is the difference \(52-15\), not a common part; and 67 is impossible because an intersection cannot contain more elements than either original set. Thus, option A is correct.
Frequently asked questions
What is the correct answer to this question?
15
Why is this the correct answer?
Because \(A\subseteq B\), every element of A is also an element of B. The elements common to A and B are therefore exactly the elements of A, so \(A\cap B=A\). It follows that \(n(A\cap B)=n(A)=15\). The value 52 is the size of B, not the intersection; 37 is the difference \(52-15\), not a common part; and 67 is impossible because an intersection cannot contain more elements than either original set. Thus, 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).
