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Sets and Relations — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsSets and Relations1 Mark
MCQ
If set $A$ is empty set then $n[P[P[P(A)]]]$ is
  • A
    $6$
  • B
    $16$
  • C
    $2$
  • ✓
    $4$
✓

Answer

Correct option: D.
$4$
(D) $4$
Hint:
$A=\Phi $
$\therefore n(A)=0 $
$\therefore n[P(A)]=2^{n(A)}=2^0=1$
$\therefore n[P[P(A)]]=2^{n[P(A)]}=2^1=2$
$\therefore n[P[P[P(A)]]]=2^{n[P[P(A)]]}=2^2=4$

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