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

Explanation

Since `1+a*a=1+a^(2) gt 0, AA a in S, :. (a,a) in R`
` :. ` R is reflexive
Also `(a,b) in R implies 1+ab gt 0implies ba gt 0 implies (b,a) in R,`
` :. ` R is symmetric
` :' (a,b) in R " and " (b,c) in R` need not imply `(a,c) in R.`
As `(0.25,-3) in R` and `(-3,-4) in R, " but " (0.25,-4) notin R.`
So, R is not transitive