HOW TO WRITE A RELATION AS A SET OF ORDERED PAIRS

Question :

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)}

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