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.