Question

if A={1,3,5} how many elements has P(A) ?​

Answer 1

Answer:

8

Step-by-step explanation:

because there r 3 elements so the according to formula ie 2^n (n =no of elements)it comes as 2^3=8.........

hope it helps u

Answer 2

If A = { 1 , 3 , 5 } then number of elements in P(A) is 8

Given :

The set A = { 1 , 3 , 5 }

To find :

The number of elements in P(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 :

Write down the given set

Here the given set is A = { 1 , 3 , 5 }

Step 2 of 2 :

Find number of elements in P(A)

We know that the collection of all subsets of a non empty set A is a set of sets. This set is called the power set of A and is denoted by P(A)

∴ P(A) = { Φ, {1} , {3} , {5} , {1,3} , {1,5} , {3,5} , {1,3,5}}

Hence number of elements in P(A) is 8

Note :

In another way number of elements in P(A) can be calculated

A = { 1 , 3 , 5 }

Number of elements in A = 3

We know that if a set contains n elements then number of elements in power set of the set is 2ⁿ

Hence number of elements in P(A) = 2³ = 8

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