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
$=134217728-1-27$
$=134217700$