How to Write a Relation as a Set of Ordered Pairs :
Here we are going to see how to write a relation a set of ordered pairs.
Question 1 :
A relation R from the set {2, 3, 4, 5, 6} to the set {1, 2, 3} defined by x = 2y
Solution :
Let the given sets be A = {2, 3, 4, 5, 6} and B = {1, 2, 3}. Now we have to find the relation from A to B.
Given that :
x = 2y ==> y = x/2
If x = 2, then y = 2/2 = 1 ==> (2, 1)
If x = 3, then y = 3/2 ∉ B
If x = 4, then y = 4/2 = 2 ==> (4, 2)
If x = 5, then y = 5/2 ∉ B
If x = 6, then y = 6/2 = 3 ==> (6, 3)
R = {(2, 1) (4, 2) (6, 3)}
(ii) A relation R on the set {2, 3, 4, 5, 6, 7} defined by (x, y) ∈ R <=> x is relatively prime to y.
Solution :
Relatively prime means, the greatest common divisor for the elements will be 1.
R = {(2, 3) (2, 5) (2, 7) (3, 2) (3, 4) (3, 5) (3, 7) (4, 5) (4, 3) (4, 7) (5, 2) (5, 4) (5, 6) (5, 7) (6, 5) (6, 7) (7, 2) (7, 3) (7, 4) (7, 5) (7, 6)}
(iii) A relation R on the set {0, 1, 2, 3, 4, ............10} defined by 2x + 3y = 12
Solution :
2x + 3y = 12
3y = 12 - 2x
y = (12 - 2x)/3
y = 4 - (2x/3)
If x = 0, then y = 4
If x = 1, then y = 4 - (2/3) ∉ the given set
If x = 3, then y = 2
If x = 6, then y = 0
If x = 9, then y = -2 ∉ the given set
So the relation R = {(0, 4) (3, 2) (6, 0)}
(iv) A relation R from a set A = {5, 6, 7, 8} to the set B = {10, 12, 15, 16, 18} defined by (x, y) ∈ R <=> x divides y.
Solution :
We may divide 10 and 15 by 5, 12 and 18 by 6.
So the relation be R = {(5, 10) (5, 15) (6, 12) (6, 18) (8, 16)}
After having gone through the stuff given above, we hope that the students would have understood "How to Write a Relation as a Set of Ordered Pairs".
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
©All rights reserved. onlinemath4all.com
Apr 29, 24 08:51 AM
Apr 28, 24 10:10 AM
Apr 28, 24 05:42 AM