Question # 01: Four option are given against each statement. Encircle the correct option.
\((v)\) \(\;\) If \(A\subseteq B\) and \(B-A\neq \phi\), then \(n( B-A)\) is equal to
\( a) \quad \) \(0 \)
\( b) \quad \) \(n(B)\)
\(c) \quad \) \( n(A)\)
\( d) \quad \) \( n(B)-n(A)\)
Answer: \( d) \; \) \( n(B)-n(A)\)
Explanation:
\(A\subseteq B\) means that every element of set \(A\) is also in set \(B\) i.e. fully inside.
\(B-A\neq \phi\) means that set \(B\) has some extra elements that are not in \(A\).
So, \( n( B-A)=n(B)-n(A)\).
Example:
Let, \(A=\{1,2,3\}\), \(B=\{1,2,3,4\}\)
\(B−A=\{4\}\)
\(n(B-A)=1;\) \(\;\) \(n(B)=4;\) \(\; n(A)=3\)
So, \( n(B-A)=n(B)-n(A))\)