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Question

If the relation is defined on R{0} by (x,y)Sxy>0, then S is ________

A
an equivalence relation
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B
symmetric only
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C
reflexive only
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D
transitive only
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Solution

The correct option is A an equivalence relation
sxy
for (x,x) on relation
sxy
and x2>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.


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