HOW TO WRITE POWER SET FOR THE GIVEN SET

Power Set :

The set of all subsets of a set A is called the power set of ‘A’. It is denoted by P(A).

(i) If n(A)  =  m, then n[P(A)]  =  2m.

(ii) The number of proper subsets of a set A is

n [P(A)] – 1  =  2– 1

Solved Questions

Question 1 :

Write down the power set of the following sets.

(i) A = {a, b}

Solution :

Subset of A are

=  { { }, {a}, {b}, {a, b} }

(ii) B = {1, 2, 3}

Solution :

Subset of B are

=  { { }, {1}, {2}, {3}, {1, 2}, {2, 3} {3, 1} {1, 2, 3} }

(iii) D = {p, q, r, s}

Solution :

Subset of D are

=  {{ }, {p}, {q}, {r}, {s}, {p, q}, {p, r}, {p, s}, {q, r}, {q, s} {r, s}, {q, r, s} {p, q, r, s}}

(iv) E = ∅

Solution :

P(E)  =  { { } }

Question 2 :

Find the number of subsets and the number of proper subsets of the following sets.

(i) W  =  {red, blue, yellow}

Solution :

The number of proper subsets of a set A is

n [P(A)] – 1 = 2m–1

n(A)  =  3

n [P(A)] – 1 = 23–1

=  8 - 1

Number of proper subset :

n [P(A)] – 1  =  7

(ii) X = { x2 : x ∈ N, x2 ≤ 100}

X  =  {22, 32, 42, 52, 62, 72, 82, 92, 102}

n (X)  =  10

n [P(A)] – 1  =  210 – 1

n [P(A)]  =  1024

Number of proper subset :

Number of proper subset  =  1024 - 1  =  1023

Question 3 :

(i) If n(A) = 4, find n [P(A)].

Solution :

n(A) = 4, find n [P(A)]

n [P(A)]  =  2

=  16

(ii)  If n(A) = 0, find n [P(A)].

Solution :

n [P(A)]  =  2m

=  20

=  1

(iii) If n[P(A)] = 256, find n(A).

n [P(A)]  =  256

2=  256

2m  =  28

m  =  8

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