Each of the following defines a relation on `N :` (i)`x > y ,\ x ,\ y in N`
(ii) `x+y=10 ,\ x ,\ y in N`
(iii) `x y` is square of an integer, `x ,\ y in N`
(iv) `x+4y=10 ,\ x ,\ y in N`
Determine which of the above relations are reflexive, symmetric and transitive.

Explanation

`\text{(i) x is greater than y,x, y} \in N`




`x` is greater than `y, x, y \in N`



If `(x, x) \in R`, then `x>x`, which is not true for any `x \in N`.



Therefore, `R` is not reflexive.
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