Number of Elements in a Cartesian Product

Q. If the difference between the number of subsets of two finite sets $A$ and $B$ is $120,$ then $n(A\times B)$ is

1. $25$
2. $120$
3. $24$
4. $21$

Q.

If R is a relation on a finite set having n elements, then the number of relations on A is

1. $2^n$

2. $2^{n^2}$

3. $n^2$

4. $n^n$

Q.

Prove the following theorem:

The total number of subsets of a finite set containing n elements is 2ⁿ.

Q.

What do you mean by ordered pair and ordered triplet? Give example.

Q.

If R is a relation from a fininte set A having m elements to a fininte set B having n elements, then the number of relations from A to B is

1. $2^{mn}-1$

2. $2^{mn}$.

3. $2^{mn}$

4. $m^n$

Q.

Find the number of combinations of n different objects taken r at a time.

1. n

2. 

3. (n-1)!

4. 

Q. A={1} B={{1}, 2} andC={{1}, 2, 3}
A belongs B as A={1} and B is the subset of C.But A is not the subset of C as 1 belongs to A and 1 does not belongs to C...
I want to know if A belong B then why A can't belongs to C...

Q. If A and B are subsets of the universal set U, then which of the following is/are true?

1. A ⊂ (A ∪ B)
2. A ⊂ B ⇔ (A ∪ B) = B
3. (A ∩ B) ⊂ A
4. A - B = (A ∪ B')

Q. Let $A=\{x:x\text{is a root of the equation}{x}^3+2x^2-x-2=0\}$ and $B=\{x:x\text{is a prime divisor of 720}\},$ then $n(A\times B)$ is

1. $6$
2. $9$
3. $12$
4. $15$

Q.

Let A = {1, 2} and B = {3, 4}. Find the total number of relations from A into B.

Q. Let $A=\{1,2,3\},B=\{4,5,6,7,8\},$ $C=\{4,6,8,10,12\},$ then $n\left[\right(A\times B)-(A\times C\left)\right]=$

1. $1$
2. $12$
3. $24$
4. $6$

Q.

If n(A) = 3, m(B) = 4, then write $n(A\times A\times B).$

Q. If $A=\{5,6,7\},B=\{1,2,3,4\}$, then number of elements in set $(A-B)\times B$ is

1. $24$
2. $36$
3. $16$
4. $12$

Q. If $A$ and $B$ are two sets such that$A=\{-1,2,3\},n(A\times B)=9,$ then $n\left(B\right)$ is

1. $3$
2. $6$
3. $9$
4. $1$

Q. Let $A=\{1,2,3,4,5\},$ $B=\{4,5,6,7,8\}$ and $C=\{8,9,10,11,12\},$ then $n[A\times (B^{\prime }\cup C^{\prime }{)}^{\prime }]=$

Q. If $A\times B$ has $6$ elements and $(-3,-2),(4,4),(2,-2)$ are the elements of $A\times B$, then the correct option(s) is/are

1. $A=\{-3,2\}$
2. $B=\{-2,4\}$
3. $A\times B=\left\{\right(-3,-2),(2,-2),(4,-2),(-3,4),(2,4),(4,4\left)\right\}$
4. $B\times A=\left\{\right(-2,-3),(-2,2),(4,-3),(4,2\left)\right\}$

Q.

If the set A has p elements, B has q elements, then the number of elements in $A\times B$ is

1. $p+q$

2. $p+q+1$

3. $pq$

4. $p^2$

Q.

Name one element formed from the first letter of the elements name.

Q. If $A=\{y:|y|=3x,x\le 2,x\in N\},$
$B=\{x:x\text{is a positive even number},x<14\}$ and $C=\{1,4,8\},$ then $n\left(\right(A\times B)\cap (A\times C\left)\right)$ is

1. $8$
2. $20$
3. $36$
4. $40$

Q. State true or false:

(vii) The set of letters in your mathematics book is an infinite set.

Q. Let $Z$ be the set of integers. If $A=\{x\in Z:e^{x^3-4x^2-7x+10}=1\}$ and $B=\{x\in Z:(1-x^2\left)\right(x^2-2x-8)\ge 0\},$ then $n\left[\right(A\cup B)\times (A\cap B\left)\right]$ is

Q.

If the cardinality of a set $A$ is $4$ and that of a set $B$ is $3$ , then what is the cardinality of the set $A\Delta B$ ?

1. $1$

2. $5$

3. $7$

4. Cannot be determined as the sets A and B are not given

Q. If the sum of two coprime numbers $x,y(x<y)$ is $20,$ then the total possible number of ordered pair(s) $(x,y)$ is

Q. If the product of two coprime numbers $x$ and $y$ is $36,$ then total number of ordered pairs $(x,y)$ is

Q.

.$\left(x^3-1\right)$ can be factorised as: where $\omega$ is one of the cube roots of unity.

1. $(x-1)(x–\omega )(x+{\omega }^2)$

2. $(x-1)(x–\omega )(x-{\omega }^2)$

3. $(x-1)(x+\omega )(x+{\omega }^2)$

4. $(x-1)(x+\omega )(x-{\omega }^2)$

Q. If the cardinality of a set $A$ is $4$ and that of a set $B$ is $3$, then what is the cardinality of the set $A\Delta B$.

1. $1$
2. $7$
3. $Cannotbedetermined$
4. $5$

Q. Consider the four sets $A,B,C$ and $D$ defined as
$A=\{a:a=8({\log }_4\left(x\right){)}^3+4{\log }_{\sqrt{2}}\left(x^4\right),x>0\}$
$B=\{b:b=20+\frac{13}{({\log }_{x}2{)}^2},x>0\}$
$C=\{c\in N:c\in A\cap B\text{for same}x>0\}$
$D=\{x\in Z:(x-2{)}^2(15x^2-56x+17)<0\}$

Then the number of elements in $C\times D$ is

Q. Two finite sets have p and q elements respectively. Total number of subsets of first set is 224 more than the total number of subsets of the second set. Find the values of p and q

Q.

What is the cardinal number of the following sets?

The set of inventions: telephone, pendulum, wheel and computer.

Q. If $A$ and $B$ are two sets such that$A=\{-1,2,3\},n(A\times B)=9,$ then $n\left(B\right)$ is

1. $9$
2. $3$
3. $6$
4. $1$