Question

The following relation is defined on the set of real numbers. $aRb$ if $|a-b|>0$.

Answer 1

R is not reflexive since |a -a| = 0 and
So | a- a | > a.
Thus a (-R) a for any real numbers a
R is symmetric since if | a - b| > 0, then
|b - a | = | a - b| > 0.
Thus aRb $\Rightarrow$bRa
R is not transitive. For example.
Consider the numbers 3, 7, 3 then we have 3R7 since
|3 - 7| = 4 > 0 and 7R3 since |7-3| = 4>0.
But 3(-R) 3 since |3 -3| = 0
so that |3 - 3| > |0