Question -
Answer -
(i) A relation R from the set {2, 3, 4, 5, 6} to the set {1, 2, 3} defined by x = 2y.
Let A = {2, 3, 4, 5, 6} and B = {1, 2, 3}
Given, x = 2y where y = {1, 2, 3}
When, y = 1, x = 2(1) = 2
When, y = 2, x = 2(2) = 4
When, y = 3, x = 2(3) = 6
тИ┤ R = {(2, 1), (4, 2), (6, 3)}
(ii) A relation R on the set {1, 2, 3, 4, 5, 6, 7} defined by (x, y) тИИ R тЗФ x is relatively prime to y.
Given:
(x, y) R x is relatively prime to y
Here,
2 is co-prime to 3, 5 and 7.
3 is co-prime to 2, 4, 5 and 7.
4 is co-prime to 3, 5 and 7.
5 is co-prime to 2, 3, 4, 6 and 7.
6 is co-prime to 5 and 7.
7 is co-prime to 2, 3, 4, 5 and 6.
тИ┤ R ={(2, 3), (2, 5), (2, 7), (3, 2), (3, 4), (3, 5), (3, 7), (4, 3), (4, 5), (4, 7), (5, 2), (5, 3), (5, 4), (5, 6), (5, 7), (6, 5), (6, 7), (7, 2), (7, 3), (7, 4), (7, 5), (7, 6), (7, 7)}
(iii) A relation R on the set {0, 1, 2,тАж, 10} defined by 2x + 3y = 12.
Given,
(x, y) R 2x + 3y = 12
Where x and y = {0, 1, 2,тАж, 10}
2x + 3y = 12
2x = 12 тАУ 3y
x = (12-3y)/2
When, y = 0, x = (12-3(0))/2 = 12/2 = 6
When, y = 2, x = (12-3(2))/2 = (12-6)/2 = 6/2 = 3
When, y = 4, x = (12-3(4))/2 = (12-12)/2 = 0/2 = 0
тИ┤ R = {(0, 4), (3, 2), (6, 0)}
(iv) A relation R form a set A = {5, 6, 7, 8} to the set B = {10, 12, 15, 16, 18} defined by (x, y) тИИ R тЗФ x divides y.
Given,
(x, y) R x divides y
Where, x = {5, 6, 7, 8} and y = {10, 12, 15, 16, 18}
Here,
5 divides 10 and 15.
6 divides 12 and 18.
7 divides none of the value of set B.
8 divides 16.
тИ┤ R = {(5, 10), (5, 15), (6, 12), (6, 18), (8, 16)}