Question

if A = (a,b,c,d,e) then the no. of elements of power set of A is​

Answer 1

$\huge{\boxed{\mathtt{\purple{Answer}}}}$

${\underline{\mathtt{\red{Power \: Set}}}}$

⇝ The collection of family of all subsets of a set is called the power set of that set and is denoted by P(A)

${\underline{\mathtt{\red{To\: Find}}}}$

Number of elements in Power set of set A . A = { a , b , c , d , e }

${\underline{\mathtt{\red{Solution}}}}$

⇝ A = { a , b , c , d , e }

⇝ We know that a set having n element has subset ${\mathtt{{2}^{n} }}$ .

⇝ Here n = a , b , c , d ,e = 5

$\implies \: {2}^{5}$

$\implies \: 2 \times 2 \times 2 \times 2 \times 2$

$\red{ \implies \: 32}$

So the the number of element in power set A is 32

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Self practice question :-

Find Subsets of A = {1,2,3,4} and number of elements in power set A.

Show that n {P[P(P(φ)]} = 4

Answer 2

Step-by-step explanation:

here, we have given

A = {a,b,c,d,e}

To find : Power set of given set A

Solution : for finding the Power set ,we must know the sunsets of a given set

No of Subsets of a given set = 2^n (n is no of elements in that perticular set )

there are 5:elements are given in the set A , therefore 2^n = 2^5 = 32

Basically Power is the set of all that Subsets which formed by given set.

Power set of A ={ {a} ,{b} ,{c} ,{d} ,{e},{a,b},{b,c},{c,d},{a,c},{a,d},{b,e},{c,e},{d,e},{e,a},{a,b,c},{a,c,d},{b,c,d,},{c,d,e},{b,d,e},{b,e,a},{c,e,a},{e,a,b},{a,b,c,d},{b,c,d,e},{c,d,e,a},{d,e,a,b},{e,a,b,c},{a,c,d,e},{},{a,b,c,d,e}}