Question

If the relation is defined on $R-\left\{0\right\}$ by $(x,y)\in S\iff xy>0$, then $S$ is ________

• A. an equivalence relation
• B. symmetric only
• C. reflexive only
• D. transitive only

Answer 1

The correct option is A an equivalence relation

$s\iff xy$

for (x,x) on relation

$s\iff xy$

and $x^2>0$

so, $S$ is symmetric

if $xy>0$

thus $xy>0$

so, $S$ is reflexive.

Now, if $xy>0$

and $yz>0$

so, $xz>0$

Thus, $S$ is transitive.

So, relation is equivilance.