Let A be the set of first five natural and let R be a relation on A defined as follows: (x, y) R x ≤ y

Express R and R-1 as sets of ordered pairs. Determine also

(i) the domain of R‑1

(ii) The Range of R.

Asked by Aaryan | 1 year ago |  141

##### Solution :-

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}

Answered by Sakshi | 1 year ago

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