Question

Write power sets of the following: 

(i) {a} 

(ii) {1, 2, 3} 

(iii) {a, b} 

(iv) Φ

Answer 1

(i) {a} 

Subsets of {a} are Φ and {a}. 

Hence P{a} = {Φ, {a}} 

(ii) {1, 2, 3} 

Subsets of {1, 2, 3} are Φ, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3} and {1, 2, 3}. 

Hence, P{1, 2, 3} = {Φ, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}} 

(iii) {a, b} 

Subsets of {a, b} are Φ, {a}, {b}, {a, b} 

Hence, P{a, b} = {Φ, {a}, {b}, {a, b}} 

(iv) Φ 

Φ is null set, then P(Φ) = {Φ}