Q4,paper 2, D 12.The power set of the set {phi} is

(A) {phi}

(B) {phi, {phi}}

(C) {0}

(D) {0, phi, {phi}}

Answer (B)

Explanation.

Power set  of set A={1,2} is given by all combination of 1 and 2 with one more element phi because  phi is element of every power set, so power set of A={{},{1},{2},{1,2}}. Its comes out to be 2^n.

phi is considered to be an element in its power set like but  not in set. A cardinality is two. Power set of A cardinality is 4.  Set{phi} in question has cardinality 1.so its cardinality is two. Hence power set is {phi, {phi}}.