Question

If $X=\{1,2,3, \ldots, 10\}$ 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, \ldots, 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, \ldots, 10\}-\{4\}-\{1,2,3,5\} $
$=\{6,7,8,9,10\}$
$\therefore $ Number of subsets $B$ of $X$ i.e., $\{6,7,8,9,10\}$
$=2^{5}$