Question # 01: Four option are given against each statement. Encircle the correct option.
\((iv)\)\(\;\)If \(A\) and \(B\) are overlapping sets, then \(n(A-B)\) is equal to:
\( a) \quad \) \(n(A) \)
\( b) \quad \) \( n(B)\)
\(c) \quad \) \( A\cap B\)
\( d) \quad \) \( n(A)-n(A\cap B)\)
Answer: \( d) \; \) \( n(A)-n(A\cap B)\)
Explanation:
\(A−B\) (also called the difference of A and B) means that all elements that are in set \(A\), but not in set \(B\).
When sets overlap, it means, they have some elements in common, i.e. \(A\cap B\ne \phi\).
So, \( n(A-B)=n(A)-n(A\cap B)\).
Example:
Let, \(A=\{1,2,3,4\}\), \(B=\{3,5,6\}\)
\(A\cap B=\{3\}\)
\(A−B=\{1,2,4\}\)
\(n(A-B)=3;\) \(\;\) \(n(A)=4;\) \(\; n(A\cap B=1\)
So, \( n(A-B)=n(A)-n(A\cap B)\)