GATE CSE 2015 Set 2 | Question: 18

Question

The cardinality of the power set of $\{0, 1, 2, \dots , 10\}$ is _______

Answer 1

Answer: $2048$

• For any set $S$ having $n$ elements, the number of elements in power set $P(S)$ is $2^n$.
• The term cardinality means the number of elements present in the set.

Number of elements in set $= 11.$

Therefore, cardinality of power set $= 2^{11} = 2048.$

Answer 2

The cardinality of the power set of $\left \{ 0,1,2,..,10 \right \}$ is _______

Total number of elements in given set is $11$.

So the cardinality of the power set of given set will be $2^{11}$  _{^{$= >$}} $2048$

Answer 3

Let, A ={0,1,2,3,,,10}

| A| = 11

| p(A)| = 2^11 =2048.

 The correct answer is 2048.

Answer 4

2^11 is the number of elements in power set for this so it is 2048.