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

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⋅ q=12 (B) p+q=8 (C) p-q=3 (D) p=3q

Tardigrade Admin · Accepted Answer

Given: Number of elements of set A=p, Number of elements of set B=q Then, total number of subsets of set A=2p Total number of subsets of set B=2q Therefore, 2p-2q=56 ⇒ 2p-2q=64-8 ∴ p=6 and q=3 Hence, p-q=3 .

Q. 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

$p \cdot q = 12$

$p + q = 8$

$p - q = 3$

$p = 3 q$

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,
$2^{p} - 2^{q} = 56$
$\Rightarrow 2^{p} - 2^{q} = 64 - 8$
$∴ p = 6$ and $q = 3$
Hence, $p - q = 3$ .

Q. 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

p⋅q=12

p+q=8

p−q=3

p=3q