Show that the relations `R` on the set `R` of all real numbers, defined as `R={(a ,\ b): alt=b^2}` is neither reflexive nor symmetric nor transitive.

Explanation

R`={(a,b):a≤b^2}`

It can be observed that `(1/2,1/2)∈/R`, since `1/2>(1/2)^2=1/4.`

`\therefore `R is not reflexive.

Now,` (1,4)∈R` as` 1<4^2`

But, `4` is not less than `1^2.`

`\therefore (4,1) \!in`R

`\therefore `R is not symmetric.

Now, `(3,2),(2,1.5)∈R`

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