Question

If n[P(A)] = 32, then find the number of elements of A
​

Answer 1

Question :-

• If n[P(A)] = 32, then find the number of elements of A.

Answer

Given :-

• n[P(A)] = 32

To Find :-

• Number of elements in set A.

Concept used :-

Definition of Power Set :-

• The power set is a set which includes all the subsets including the empty set and the original set itself. It is also a type of sets.
• For example, If set A = {x,y,z} is a set, then all its subsets {x}, {y}, {z}, {x,y}, {y,z}, {x,z}, {x,y,z} and {} are the elements of powerset, such as:
• Power set of A, P(A) = {{x}, {y}, {z}, {x,y}, {y,z}, {x,z}, {x,y,z}, {} }, where P(A) denotes the powerset.

• The number of elements in set A is n, then number of elements in power set of A 2^n.

Solution :-

Let suppose that set A has n elements.

$\bf\implies \:n[P(A)] = {2}^{n}$

According to statement, n [P(A)] = 32

$\bf\implies \: {2}^{n} = 32$

$\bf\implies \: {2}^{n} = {2}^{5}$

$\bf\implies \:n = 5$

____________________________________________

Answer 2

Answer:

Solution :-

Let suppose that set A has n elements.

\bf\implies \:n[P(A)] = {2}^{n}⟹n[P(A)]=2

n

According to statement, n [P(A)] = 32

\bf\implies \: {2}^{n} = 32⟹2

n

=32

\bf\implies \: {2}^{n} = {2}^{5}⟹2

n

=2

5

\bf\implies \:n = 5⟹n=5