How many elements has P(A), if A=ø ?

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1.Set Theory

easy

How many elements has $P(A),$ if $A=\varnothing ?$

Option A

Option B

Option C

Option D

Solution

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.

Standard 11

Mathematics

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