Kenneth Rosen Edition 7 Exercise 2.1 Question 24 (Page No. 126)

Question

Determine whether each of these sets is the power set of a set, where $a$ and $b$ are distinct elements.

1. $\phi$
2. $\left \{ \phi ,\left \{ a \right \} \right \}$
3. $\left \{ \phi ,\left \{ a \right \},\left \{ \phi ,a \right \} \right \}$
4. $\left \{ \phi ,\left \{ a \right \},\left \{ b \right \},\left \{ a,b \right \} \right \}$

Answer 1

Say, Set $S=\left \{ a,b \right \}$

Power set of $S$ is $2^{S}=\left \{ \phi ,\left \{ a \right \},\left \{ b \right \} ,\left \{ a,b \right \}\right \}$

So, power set $P(S)$ is $(d)$