Question

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

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

Answer 1

Answer: (A)

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