Question

Power set of empty set has exactly __________ subset

Answer 1

Hint: Power set of any set(S) includes empty set as its subset and set S itself also. Number of subset in power set of set S having n element is ${{2}^{n}}$

Complete step-by-step solution -
In general, a power set is a set of all subsets of a given set.
For example if we have set S as S=\left\\{ 1,2 \right\\}
As set S has 2 elements , so number of subset in power set of S is ${{2}^{2}}=4$
So we can write subset of set S as given below:
\left\\{ {} \right\\},\left\\{ 1 \right\\},\left\\{ 2 \right\\},\left\\{ 1,2 \right\\}
So we can see the power set includes the empty set and the given set itself as a subset.
So in the given question we have an empty set.
So its power set should have one subset which is an empty set itself.
So option A is correct.

Note: As we discussed the number of subset in the power set given by ${{2}^{n}}$ where n is number of elements in a given set. The empty number of elements is 0. So the number of subset in the power set of an empty set is ${{2}^{0}}=1$. We can justify the answer by this way also.