Definition of Relations

Q.

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

1. Symmetric only

2. Reflexive only

3. Equivalence relation

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

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

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.

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. None of these

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

4. {(1, 3), (2, 6), (3, 9), ..}

Q.

If A = {5, 7, 9, 11}, B = {9, 10} let a R b means a < b. a $\in$ A, (a, b) $\in$ R, b $\in$ B. Then

1. Co domain of R = {9, 10}

2. Range of R = {9, 10}

3. Relation of R = {(5, 9), (5, 10), (7, 9), (7, 10), (9, 10)}

4. Domain of R = {5, 7, 9}

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. Which of the following can be the elements of a relation (R) from a set A = {1, 2, 3, 4} to set B = {a, b, c}.

1. (1, a)
2. (b, 2)
3. (2, c)
4. (c, 4)
5. (4, b)
6. (c, 1)
7. (a, 3)
8. (3, b)
9. (1, b)
10. (a, 2)

Q. Set A = {5, 9, 11} and set B = {5, 9, 10}. Let aRb be such that a<b where $a\in A,b\in Band(a,b)\in R$.

1. {5, 9, 10}
2. {5, 9, 11}
3. {9, 10}
4. {(5, 9)(5, 10)(9, 10)}

Q.

A = { 1, 2, 3, 4, 5} and B = {a, b}. The number of relations from A to B is ___ .

1. 128

2. 512

3. 1024

4. 256