Power Set

Q.

Match the following:

$$\begin{array}{cc}\text{Column A}& \text{Column B}\\ \text{1. {x: x}\in \text{R, -5 < x}\le \text{15 }}& \text{A. 1}\\ 2.A=ThepowersetP\left(A\right)has\underset{–}{}elements& B.8\\ 3.UniversasetofRationalNumbers\&IrrationalNumbers& C.RealNumbers\\ 4.No.ofelementsinPowerSetofA=\{a,b,c\}& D.Integers\\ & E.(-5,15]\\ & F.[-5,15)\end{array}$$

1. 1 - b, 2 - a, 3 - c, 4 -e

2. 1 - b, 2 - c, 3 - a, 4 -e

3. 1 - e, 2 - a, 3 - c, 4 -b

4. 1 - e, 2 - a, 3 - b, 4 -c

Q. No of elements in the power set of set A are odd, them the no of elements in the set A are

1. 5
2. None of these
3. 1
4. 3

Q. Which of the following represents the power set of Set A, where A = { - 1, 0, 1 }

1. {-1, 0}, {0, 1}, {-1, 13}, $\left\{\varphi \right\}$, {-1, 0, 1}
2. {1}, {0}, {1}, {-1, 0}, {0, 1}, {-1, 13}, $\left\{\varphi \right\}$, {-1, 0, 1}
3. {1}, {0}, {1}, {-1, 0}, {0, 1}, {-1, 13}, $\left\{\varphi \right\}$
4. {1}, {0}, {1}, {-1, 0}, {0, 1}, {-1, 13}, {-1, 0, 1}

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. The number of elements in the power set of the set $\left\{\right(a,b):a^2+b^2=7,a,b\in Z\}$ is

Q. Number of elements in the power set of an empty set is

Q. The number of elements in the power set of $A$, where $A=\{x:x\in W\text{and}{x}^3-1\le 7\}$

1. $3$
2. $16$
3. $8$
4. $64$

Q. The number of elements in power set of $A=\{1,2,3,8,9,10\}$ is

1. $32$
2. $64$
3. $36$
4. $12$

Q. The relation on the set $A=\{x:1<|x|\le 4,x\in Z\}$ is defined by $R=\left\{\right(x,y):y=|x|\}.$ Then the number of elements in the power set of $R$ is

1. $16$
2. $32$
3. $64$
4. $128$

Q. The number of subsets of the power set of $A$, where $A=\{x:x\in N-3\le |x|<4\}$ will be