GATE | GATE-CS-2015 (Set 1) | Question 65

For a set A, the power set of A is denoted by 2^A. If A = {5, {6}, {7}}, which of the following options are True.

(A) I and III only
(B) II and III only
(C) I, II and III only
(D) I, II and IV only


Answer: (C)

Explanation:

A = {5, {6}, {7}}

Below is Powerset of A
{  φ, 
   {5}, 
   {{6}}, 
   {{7}}, 
   {5, {6}}, 
   {5, {7}}, 
   {{6}, {7}}, 
   {5, {6}, {7}} 
}

I is true, as φ belongs to Powerset.

II is true, as an empty set is a subset of every set.

III is true as {5, {6}} belongs to Powerset.

IV is false, {5, {6}} is not a subset, but {{5, {6}}} is.

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