Number of Elements in a Cartesian Product

Q. $A$ can do a piece of work in $4$ hours; $B$ and $C$ together can do it in $3$ hours, while $A$ and $C$ together can do it in $2$ hours. How long will $B$ alone take to do it?

1. $8$ hours
2. $10$ hours
3. $12$ hours
4. $24$ hours

Q.

If set A = {1, 2, 3} and set B = {2, 3, 5, 7}. Then the number of elements in A $\times$ B is ___

Q. For any two sets A and B, $\left\{\right(A\setminus B)\cup (B\setminus A\left)\right\}\cap (A\cap B)$ is:

1. $\varphi$
2. $A\cup B$
3. $A\cap B$
4. $A^{\prime }\cap B^{\prime }$

Q.

Given two finite sets A and B such that n(A) = 3, n(B) = 3. Then total number of relations from A to B is _____.

1. 4

2. 8

3. 512

4. 6

Q.

If set A has p element and set B has q elements, then the number of element in set (A $\times$ B) is _____.

1. 

2. 

3. 

4. 

Q.

Let A = {1, 2, 3}. The total number of distinct relations that can be defined over A is

1. 2⁹

2. 6

3. 8

4. None of these

Q. How do you simplify $15÷5(8-6+3)\times 5$?

Q. If a : b = c : d, prove that:
xa + yb : xc + yd = b : d