Question -
Answer -
A is set of first five natural numbers.
So, A= {1, 2, 3, 4, 5}
Given: (x, y) R x ≤ y
1 is less than 2, 3, 4 and 5.
2 is less than 3, 4 and 5.
3 is less than 4 and 5.
4 is less than 5.
5 is not less than any number A
∴ R = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (2, 2), (2, 3), (2, 4), (2, 5), (3, 3), (3, 4), (3, 5), (4, 4), (4, 5), (5, 5)}
“An inverse relation is the set of ordered pairs obtained by interchanging the first and second elements of each pair in the original relation. If the graph of a function contains a point (a, b), then the graph of the inverse relation of this function contains the point (b, a)”.
∴ R-1 = {(1, 1), (2, 1), (3, 1), (4, 1), (5, 1), (2, 2), (3, 2), (4, 2), (5, 2), (3, 3), (4, 3), (5, 3), (4, 4), (5, 4) (5, 5)}
(i) Domain of R 1 = {1, 2, 3, 4, 5}
(ii) Range of R = {1, 2, 3, 4, 5}