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Question

If the relation is defined on R by (x,y)Sxy0, 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


Explanation for the correct option.

Step 1: For reflexive

Given, a relation is defined on R by (x,y)Sxy0.

For reflexive.

Let x,xS

x20

So, the relation is reflexive.

Step 2: For symmetric

For symmetric.

Let x,yS then xy0

yx0

So, the relation is symmetric.

Step 3: For transitive

For transitive.

Let x,yS then xy0 and y,zS then yz0.

xz0 i.e; x,zS

So, the relation is transitive.

As the relation is reflexive, symmetric & transitive so it is an equivalence relation.

Hence, option A is correct.


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