Question

For a set $Y,$ if $P\left(Y\right)=\{\varnothing ,\{2\},\{\left\{4\right\}\},\{2,\left\{4\right\}\left\}\right\},$ then $Y=$

• A. $\{2,\{4\left\}\right\}$
• B. $\{2,4\}$
• C. $\left\{\right\{2\},4\}$

Answer 1

The correct option is A $\{2,\{4\left\}\right\}$

For a set $X,$ it's power set is given as:
$P\left(X\right)=\{\varnothing ,\{2\},\{\left\{4\right\}\},\{2,\left\{4\right\}\left\}\right\}$
Now, we know power set of a set is the set of all the subsets of the set.
Looking closely at the power set, we can see $X=\{2,\{4\left\}\right\}.$