Question

For any set $M$ if $M\cup \varnothing =\varnothing ,$ then

• A. $M=\varnothing$
• B. $n\left(M\right)=1$
• C. $n\left(P\right(M\left)\right)=2$

Answer 1

The correct option is A $M=\varnothing$

Given a set $M:M\cup \varnothing =\varnothing$
Now, according to the identity law any set $A;A\cup \varnothing =A$
$\Rightarrow M\cup \varnothing =M=\varnothing .$
$\Rightarrow n\left(M\right)=0andn\left(P\right(M\left)\right)=2^0=1$