Question

If S={10,20,30,40}, then find P(S)​

Answer 1

If S = {10 , 20 , 30 , 40 } then P(S) ={Φ, {10}, {20},{30},{40},{10,20},{10,30},{10,40},{20,30},{20,40},{30,40},{10,20,30},{20,30,40},{30,40,10},{40,10,30},{10,20,30,40}}

Given :

The set S = {10 , 20 , 30 , 40 }

To find :

The set P(S)

Solution :

Step 1 of 2 :

Define power set of a 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)

Step 2 of 2 :

Find P(S) for the set S

Here the given set is S = {10 , 20 , 30 , 40 }

We know that if a set S contains n elements then the number of subsets of S

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

By the given number of elements in S = 4

So number of elements in P(S) = 2⁴ = 16

Now the power set P(S) , the set of all subsets of S is given by

P(S) ={Φ, {10}, {20},{30},{40},{10,20},{10,30},{10,40},{20,30},{20,40},{30,40},{10,20,30},{20,30,40},{30,40,10},{40,10,30},{10,20,30,40}}

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