Students can practice various questions from Relation to get grip on the concepts. This Worksheet on Math Relation covers various topics like Mapping for Relations, Representing Relations using a set of ordered pairs, arrow diagrams, etc. Solve the Ample Problems provided in the Math Relation Worksheet and get a better idea of the concepts within it. Practice the problems on your own and cross-check your solutions with the step by step solutions provided to understand where you went wrong.

1. If A= {3, 4, 5, 6, 7, 8}, B = {9, 10, 11, 12}. What is the number of elements in AxB?

**Solution:**

Given n(A) = 6

n(B) = 4

n(AxB) = 24

2. Determine the domain and range of the given function

{11, -5), (8, -3), (5, 2), (7, 6), (6, -10)}

Range =_____

Domain = _____

**Solution:**

Given Function is {11, -5), (8, -3), (5, 2), (7, 6), (6, -10)}

Domain is the first component of the ordered pairs and second component in the ordered pairs is the Range.

Domain = {11, 8, 5, 7, 6}

Range = {-5, -3, 2, 6, -10}

3. Represent Relation {(-3, 3) (0, -5) (2, 0) (6, 0)} using an Arrow Diagram?

**Solution:**

Take the Domain Values on the left column and Range Values in the Right Column and mark the relation between them using arrows.

4. Let A = {10, 15, 18, 21, 24} B = { 3, 5, 6, 7} be two sets and let R be a relation from A to B ‘is multiple of’. Represent in the Set of Ordered Pairs?

**Solution:**

R = {(10, 5) (15, 3) (18, 3) (18, 6) (21, 3) (21, 7) (24, 6)}

5. Given the relation R = {(3,4), (7,-1), (x,7), (-3,-4)}. Which of the following values for x will make relation R a function?

(a) 8

(b) 7

(c) -3

(d) 3

**Solution:**

(a) 8

To make relation R a Function we need to have a value that doesn’t repeat with the first components of the ordered pairs. Therefore, among all the options 8 is the value that is unique.

6. State whether the following statements are true or false

(i) All Functions are Relations

(ii) All Relations are Functions

(iii) A relation is a set of input and output values that are related in some way

**Solution:**

(i) True

(ii) False

(iii) True

7. Express the Relation as a Set of Ordered Pairs?

**Solution:**

Expressing the above Relation as a Set of Ordered Pairs we get

R = {(-4, 0) (-4, 9) (-4, 11)}

8. If A = {u, v, w} and B = {x, y}, find A × B and B × A. Check whether the two products equal or not?

**Solution:**

Given A = {u, v, w} and B = {x, y}

AxB = {(u,x) (u, y) (v,x) (v,y) (w, x) (w, y)}

BxA = {(x,u) (y, u) (x, v) (y, v) (x, w) (y, w)}

AxB and BxA don’t have the same ordered pairs.

Therefore, AxB ≠ BxA.

9. If (u/2 + 1, v+2) = (1, 2/5), find the values of u and v?

**Solution:**

Given (u/2 + 3, v+2) = (1, 2/5)

As per the Equality of Ordered Pairs we have

u/2+3 = 1

u/2 = 1-3

u/2 = -2

u = -2*2

u = -4

v+2 = 2/5

v = 2/5-2

v =(2-4) /5

v = -2/5

Therefore, values of u and v are -4, -2/5.

10. Range is the Set of _____ when it comes to Relations in Math?

**Solution:**

The range is the set of y-values when it comes to Relations in Math.