Power Set of a Set

Q.

Let $\mathrm{M}$ be any $3\times 3$ matrix with entries from the set $\{0,1,2\}$ .The maximum number of such matrices, for which the sum of diagonal elements of $M^{T}M$ is seven, is

Q. The elements of power set of Set $A=\{-1,0,1\}$ are

1. $\left\{1\right\},\left\{0\right\},\left\{1\right\},\{-1,0\},\{0,1\},\{-1,1\},\{-1,0,1\}$
2. $\{-1,0\},\{0,1\},\{-1,1\},\varphi ,\{-1,0,1\}$
3. $\left\{1\right\},\left\{0\right\},\left\{1\right\},\{-1,0\},\{0,1\},\{-1,1\},\varphi ,\{-1,0,1\}$
4. $\left\{1\right\},\left\{0\right\},\left\{1\right\},\{-1,0\},\{0,1\},\{-1,1\},\varphi$

Q. The power set of $C=\left\{\varphi \right\}$ is

1. $\left\{\varphi \right\}$
2. $\{\varphi ,\{\varphi \left\}\right\}$
3. $\left\{\right\{\varphi \left\}\right\}$
4. $\left\{0\right\}$

Q. Power set of a set $X$ is a set of all the subsets of $X.$

1. False
2. True

Q. For a set $X=\{2,3,\{2,3\left\}\right\},P\left(X\right)=$

1. $\left\{\right\{2\},\{3\},\{\{2,3\}\left\}\right\}$
2. $\{\varnothing ,\{2\},\{3\},\{\{2,3\}\left\}\right\}$
3. $\{\varnothing ,\{2\},\{3\},\{\{2,3\}\},\{2,\{2,3\}\},\{3,\{2,3\}\left\}\right\}$
4. $\{\varnothing ,\{2\},\{3\},\{\{2,3\}\},\{2,\{2,3\}\},\{3,\{2,3\}\},\{2,3,\{2,3\}\left\}\right\}$

Q. For a set $Y,$ if $P\left(Y\right)=\{\varnothing ,\{2\},\{\left\{4\right\}\},\{2,\left\{4\right\}\left\}\right\},$ then $Y=$

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

Q. Let set $R=\{P:B\subseteq P\subseteq A\}$
If $A=\{1,2,3,4,5\}$ and $B=\{1,2\}$, then number of elements in set $R$ is

1. $2$
2. $4$
3. $8$
4. $16$

Q. The elements of power set of Set $A=\{-1,0,1\}$ are

1. $\left\{1\right\},\left\{0\right\},\left\{1\right\},\{-1,0\},\{0,1\},\{-1,1\},\{-1,0,1\}$
2. $\{-1,0\},\{0,1\},\{-1,1\},\varphi ,\{-1,0,1\}$
3. $\left\{1\right\},\left\{0\right\},\left\{1\right\},\{-1,0\},\{0,1\},\{-1,1\},\varphi ,\{-1,0,1\}$
4. $\left\{1\right\},\left\{0\right\},\left\{1\right\},\{-1,0\},\{0,1\},\{-1,1\},\varphi$

Q. The power set of the set $A=\{a,b,c\}$ is

1. $\left\{\right\{a\},\{b\},\{c\},\{a,b\},\{b,a\},\{a,c\},\{a,b,c\left\}\right\}$
2. $\{\varnothing ,\{a\},\{b\},\{c\},\{a,b\},\{b,a\},\{a,c\},\{a,b,c\left\}\right\}$
3. $\{\varnothing ,\{\left\{a\right\},\left\{b\right\},\left\{c\right\},\{a,b\},\{b,a\},\{a,c\}\left\}\right\}$

Q. If $A=\{1,2,\{3,4\left\}\right\}$, then the number of elements in $P\left(P\right(A\left)\right)$ is
(where $P\left(A\right)$ is the power set of $A)$

Q. Let set $R=\{P:B\subseteq P\subseteq A\}$
If $A=\{1,2,3,4,5\}$ and $B=\{1,2\}$, then number of elements in set $R$ is

1. $2$
2. $4$
3. $8$
4. $16$

Q. The power set of $C=\left\{\varphi \right\}$ is

1. $\left\{\varphi \right\}$
2. $\{\varphi ,\{\varphi \left\}\right\}$
3. $\left\{\right\{\varphi \left\}\right\}$
4. $\left\{0\right\}$

Q. The power set of the set $D=\varnothing$ is

1. $\left\{\varnothing \right\}$
2. $\varnothing$
3. $\left\{\right\{\varphi \left\}\right\}$

Q. For a set $Y,$ if $P\left(Y\right)=\{\varnothing ,\{2\},\{\left\{4\right\}\},\{2,\left\{4\right\}\left\}\right\},$ then $Y=$

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

Q. Power set of a set $X$ is a set of all the subsets of $X.$

1. False
2. True