Question

Two finite sets $A$ and $B$ have $p$ and $q$ elements respectively. If total number of subsets of set $A$ is $56$ more than total number of subsets of set $B$ , then

• A. $p\cdot q=12$
• B. $p+q=8$
• C. $p-q=3$
• D. $p=3q$

Answer 1

Answer: (C)

Given:
Number of elements of set $A=p$,
Number of elements of set $B=q$
Then, total number of subsets of set $A=2^{p}$
Total number of subsets of set $B=2^{q}$
Therefore,
$2^{p}-2^{q}=56$
$\Rightarrow 2^{p}-2^{q}=64-8$
$\therefore p=6$ and $q=3$
Hence, $p-q=3$ .