Question

if A={1,2,3,4} then find the number of elements in power set of A .

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Answer 1

Answer:

No. of elements in power set of A = Total subsets of A

$so \: required \: no \: = {2}^{no. \: of \: elements \: in \: set} = {2}^{4} = 16 \: ans.$

Answer 2

Number of elements in power set of A = 16

Given :

A = { 1 , 2 , 3 , 4 }

To find :

The number of elements in power set of A

Concept :

Power Set

The collection of all subsets of a non empty set S is a set of sets. This set is called the power set S and is denoted by P(S)

Solution :

Step 1 of 2 :

Find number of elements in A

Here the given set is A = { 1 , 2 , 3 , 4 }

Number of elements in A = 4

Step 2 of 2 :

Find number of elements in power set of A

We know that if a set A contains n elements then the number of subsets of A $\sf = {2}^{n}$

Number of elements in A = n = 4

The number of elements in power set of A

$\sf = {2}^{n}$

$\sf = {2}^{4}$

$\sf = 16$

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