Power Set

Q.

If $A=\left\{1,2,3\right\}$, the number of elements in a power set is __________.

Q. Assume that $P\left(A\right)=P\left(B\right)$. Show that $A=B$.

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.

If a set contains n elements, then write the number of elements in its power set.

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

Q. List all the subsets of the set $\{-1,0,1\}.$

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

Q.

Write the number of elements in the power set of null set.

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.

If $(x,y)$ is the solution of the following equations ${\left(2x\right)}^{\log 2}={\left(3y\right)}^{\log 3}\mathrm{and}{3}^{\log x}=2^{\log y}$, then $x$ is equal to

1. $\frac{1}{6}$

2. $\frac{1}{3}$

3. $\frac{1}{2}$

4. $6$

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.

If $A=\{x,y\}$ then the power set of $A$ is

Q. Range of f(x)=20 power x is

Q.

Two finite sets have $m$ and $n$ elements respectively. The total number of subsets of the first set is $48$ more than the total number of subsets of the second set and $f=I-\left\{N\right\}$ then $f(m+n)$ is

1. $9$

2. $10$

3. $48$

4. $15$

Q. The cardinality of the Power Set of $\{\varphi ,\left\{\varphi \right\},\{\varphi ,\left\{\varphi \right\}\}\}$

1. Cannot be less than 8.
2. Is equal to $6$
3. Is equal to $8$
4. Can be less than $8$.

Q. Let A ={x, y, z} and B={1, 2}. Find the number of relations from A to B.

Q. 13. Integration of e raise to the power x-[x] and tge limits are upper limit 1000 lower limit 0

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

1. $2$
2. $4$
3. $8$
4. $10$

Q. If $A=\{\varphi ,\left\{\left(\varphi \right)\right\}\}$, then the power set $P\left(A\right)$ of $A$ is

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

Q. Two finite sets have $m,n$ elements respectively. The total number of subsets of the first set is $224$ more than the total number of subsets of the second. The values of $m$ and $n$ are

1. $4,8$
2. $5,7$
3. $8,5$
4. $8,7$

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. If $X$ is a finite set. Let $P\left(X\right)$ denote the set of all subsets of $X$ and let $n\left(X\right)$ denote the number of elements in $X$. If for two finite subsets $A,B,n\left(P\right(A\left)\right)=n\left(P\right(B\left)\right)+15$ then the ordered pair $\left(n\right(A),n(B\left)\right)=$

1. $(6,2)$
2. $(8,4)$
3. $(4,0)$
4. $(0,1)$

Q. If the cardinal number of the set $A$ is $1$, then the cardinal number of the power set $P\left(A\right)$ is:

1. $0$
2. $2$
3. $1$
4. $3$

Q. Two finite sets have $m$ and $n$ elements. The number of elements in the power set of the first set is $48$ more than the total number of elements in the power set of the second set then, the values of $m$ and $n$ are :

1. $6,3$
2. $6,4$
3. $7,4$
4. $7,6$

Q. If A is a finite set, let P(A) denote the set of all subsets of A and n(A) denote the number of elements in A. If for two finite sets X and Y, $n\left[P\right(X\left)\right]=n\left[P\right(Y\left)\right]+15$ then find n(X) and n(Y).

1. $n\left(X\right)=4;n\left(Y\right)=0$
2. $n\left(X\right)=0;n\left(Y\right)=4$
   
3. $n\left(X\right)=4;n\left(Y\right)=4$
   
4. $n\left(X\right)=0;n\left(Y\right)=0$
   

Q. If $A$ be a finite set having n elements and $P\left(A\right)$ is its power set then total number of subsets of $P\left(P\right(A\left)\right)$ is

1. $2^n$
2. $4^n$
3. $2^{2^n}$
4. $2^{2n}$

Q. The number of non-empty proper subsets of a set containing 7 elements is______

1. 127
2. 128
3. 126
4. None of these

Q. A set contains n elements. The power set of this set contains

1. $n^2$ elements
2. $2^{\frac{\lambda }{2}}$ elements
3. n elements
4. $2^n$ elements

Q. If $A=\{1,3,5,7\}$, then what is the cardinality of the power set $P\left(A\right)$?

1. $8$
2. $15$
3. $16$
4. $17$