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

Explanation

`R={(a,b):a le b^(2)}`
Here `(1,1) in R " as " 1 le 1, " but " 0.5 notin R " as " 0.5 gt (0.5)^(2)`
Therefore, R is not reflexive.
Now, `(1,4) in R " as " 1 lt 4^(2)`
But, 4 is not less than 1.
Therefore, `(4,1) notin R`
Therefore, R is not symmetric.
Further, `(3,2),(2,1.5) in R ("as "3 lt 2^(2) " and " 2 lt (1.5)^(2))`
But, ` 3 gt (1.5)^(2)=2.25`
Therefore, `(3,1.5) notin R`
Therefore, R is not transitive.
Hence, R is neither reflexive, nor symmetric, nor transitive.