Question

Suppose $P,Q$ and $R$ are three sets, each with three elements. The number of subsets of the set $P\times Q\times R$ , that have at least $2$ elements is

• A. $134217700$
• B. $134217701$
• C. $134217727$
• D. $134217728$

Answer 1

Answer: (A)

$n(P)=3$,
$n(Q)=3$,
$n(R)=3$
$\therefore n(P\times Q\times R)$
$=3\times 3\times 3=27$
Total number of subsets of $(P\times Q\times R)=2^{27}$
$=134217728$
$\therefore$ Number of subsets of the set $(P\times Q\times R)$ that have at least $2$ elements
$=134217728-1-27$
$=134217700$