How many elements has $P(A),$ if $A=\varnothing ?$
How many elements has $P(A),$ if $A=\varnothing ?$
We know that if $A$ is a set with $m$ elements i.e., $n(A)=m,$ then $n[p(A)]=2^{m}$
If $A=\varnothing,$ then $n(A)=0$
$\therefore n[P(A)]=2^{0}=1$
Hence, $P(A)$ has one element.
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- [JEE MAIN 2021]