Definition of relations

Q.

A relation from P to Q is

1. A universal set of P × Q

2. P × Q

3. An equivalent set of P × Q

4. A subset of P × Q

Q. Two sets A and B have p and q elements respectively. Then the number of relations from B to A is

1. $pq$
2. $q^p$
3. $p+q$
4. $2^{pq}$

Q.

Which of the following are relations from the set $A=\{1,2,3,4\}$ to set $B=\{a,b,c\}$?

1. $\left\{\right(1,a),(1,b),(1,c\left)\right\}$

2. $\left\{\right(2,a),(2,b),(2,c\left)\right\}$

3. $\left\{\right(3,a),(3,b),(3,c\left)\right\}$

4. $\left\{\right(4,a),(4,b),(4,c\left)\right\}$

Q.

The relation R defined on the set of natural numbers as {(a, b) : a differs from b by 3}, is given by

1. {(1, 4, (2, 5), (3, 6), .....}

2. {(4, 1), (5, 2), (6, 3), .....}

3. {(1, 3), (2, 6), (3, 9), ..}

4. None of these

Q.

Let X = {1, 2, 3, 4, 5} and Y = {1, 3, 5, 7, 9}. Which of the following is/are relations from X to Y

1. $R_1=\left\{\right(x,y)y=2+x,x\in X,y\in Y\}$

2. $R_2=\left\{\right(1,1),(2,1),(3,3),(4,3),(5,5\left)\right\}$

3. $R_3=\left\{\right(1,1),(1,3),(3,5),(3,7),(5,7\left)\right\}$

4. $R_4=\left\{\right(1,3),(2,5),(2,4),(7,9\left)\right\}$

Q.

If $A=\{5,7,9,11\},B=\{9,10\}$ and $aRb$ means $a<b$ where $a\in A,b\in B,$ then which of the following are true?

1. Co-domain of $R$ is $\{9,10\}.$

2. Range of $R=$Co-domain of $R$

3. $R=\left\{\right(5,9),(5,10),(7,9),(7,10),(9,10\left)\right\}$

4. Domain of $R$ is $\{5,7,9\}.$

Q.

With reference to a universal set, the inclusion of a subset in another, is relation, which is

1. Symmetric only

2. Equivalence relation

3. Reflexive only

4. None of these