Let a relation `R_1` on the set R of real numbers be defined as `(a , b) in R iff 1+a b >0` for all `a , b in Rdot` Show that `R_1` is reflexive and symmetric but not transitive.

Explanation

`R_1 = {(a,b) in R<=> 1+ab gt 0`

First we will check `R` for reflexive.

For, `(a,a) in R `,

`=>1+a^2 gt 0`, which is true.

So, `R` is reflexive.


Now, we will check for symmetric.

For, `(a,b) in R`,

...