Question

What is universal and power set?

Answer 1

Universal and power sets.

A universal set is defined to be a set that includes all of the elements or objects of other sets, as well as its own. The letter '$\mathrm{U}$' is commonly used to represent it.

The set of all subsets of a Set $A$, including the Set itself and the null or empty set, is called the power set. It is denoted as $P\left(A\right)$.

For example: if A and B are two sets, such as $A=\{1,2,3\}$ and $B=\{a,b,c\}$, then the universal set associated with these two sets is given by $U=\{1,2,3,a,b,c\}$.

The power set of set $A$ is,

$P\left(A\right)=\{\varnothing ,\{1\},\{2\},\{3\},\{1,2\},\{2,3\},\{1,3\},\{1,2,3\left\}\right\}$

Hence the universal set '$\mathrm{U}$' is the set including all the elements, objects and the power set $P\left(A\right)$ is the set of the subsets of $A$.