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

Answer 1

Answer: (A)

$2^5$

Answer 2

The correct option is(A): 25.

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., $\\{6,7,8,9,10\\}$
$=2^{5}$.