Determine whether Relation `R` on the set `N` of all natural numbers defined as `R={(x ,\ y): y=x+5` and `x<4}` is reflexive, symmetric or transitive.

Explanation

`R={(x,y):y=x+5andx<4}={(1,6),(2,7),(3,8)}`


It is seen that` (1,1)∈/R \rightarrow `R is not reflexive.

Also` (1,6)∈R. `

But,` (1,6) \!in R.`

`\therefore `R is not symmetric.


Now, since there is no pair in R such that` (x,y) `and `(y,z)∈R,` then` (x,z)` cannot belong to R.
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