Question

If $X=\{1,2,3,...,10\}$ and $A=\{1,2,3,4,5\}$. Then, the number of subsets $B$ of $X$ such that $A-B=\left\{4\right\}$ is

• A. $2^5$
• B. $2^4$
• C. $2^5-1$
• D. $1$
• E. $2^4-1$

Answer 1

The correct option is A $2^5$

Given, $X=\{1,2,3,....,10\}$
and $A=\{1,2,3,4,5\}$
Now, $A-B=\left\{4\right\}$
$\Rightarrow B=A-\left\{4\right\}=\{1,2,3,4,5\}-\left\{4\right\}$
$=\{1,2,3,5\}$
$\therefore X-\left\{4\right\}-B$
$=\{1,2,3,...,10\}-\left\{4\right\}-\{1,2,3,5\}$
$=\{6,7,8,9,10\}$
Therefore,number of subsets $B$ of $X$ i.e., $\{6,7,8,9,10\}$ $=2^5$.