Question

let A=the Set Of Natural Numeber. If R a Relation From A To A Such That R={(x,y): 2x+y=10} Then Find All Elements Of R

Answer 1

The elements of the relation R = {(x, y): 2x + y = 10} are the ordered pairs (1, 8), (2, 6), (3, 4), and (4, 2), where both x and y are natural numbers.

Step-by-step explanation:

The question is asking to find the set of ordered pairs (x, y) that satisfy the relation R = {(x, y): 2x + y = 10}, where both x and y are natural numbers.

To find the elements of R, we can list out natural numbers for x starting from 1 and find the corresponding y such that the equation holds.

1. When x = 1, 2(1) + y = 10 → y = 8, thus (1, 8) ∈ R.
2. When x = 2, 2(2) + y = 10 → y = 6, thus (2, 6) ∈ R.
3. When x = 3, 2(3) + y = 10 → y = 4, thus (3, 4) ∈ R.
4. When x = 4, 2(4) + y = 10 → y = 2, thus (4, 2) ∈ R.

We cannot continue further with natural numbers for x since the resulting y would not be natural (y would be 0 or negative, which is not in the set of natural numbers).

Therefore, the elements of the relation R are {(1, 8), (2, 6), (3, 4), (4, 2)}.