Question

if A =(2,3,(4)), then number of elements in P(A) is equal to a.3 b.9 c. 8 d. 16​

Answer 1

answer has given in attachment

Answer 2

SOLUTION

GIVEN

A = { 2 , 3 , { 4 } }

TO DETERMINE

The number of elements in P(A)

CONCEPT TO BE IMPLEMENTED

SET :

A set is a well defined collection of distinct objects of our perception or of our thought to be conceived as a whole

SUBSET :

A set S is said to be a subset of T if every element of S is an element of T

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)

EVALUATION

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

We know that the collection of all subsets of the non empty set A is the power set A

Since A contains 3 elements

So the number of elements in P(A)

$= {2}^{3}$

= 8

= 8

More precisely

P(A)

= { Φ , { 2 } , { 3 } , { 4 } , { 2 , 3 } , { 2 , { 4 } , { 3 , { 4 } , { 2 , 3 , { 4 } } }

So the number of elements in P(A) = 8

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