Ankur Dubey Student Expert 11th Nov, 2020

Hello

1. R is reflexive

Now, ab=0

So, a=0 or b=0 (either a or b can be zero but both cannot be zero)

Thus, aRa => a.a=0 => a is not necessarily 0.

So, R is not reflexive.

2. R is symmetric

We know that, ab=ba (communicative property of multiplication)

=> aRb = ab= 0 = bRa.

So, R is symmetric.

3. R is transitive

Let aRb and bRc be arbitrary such that ab=0 and bc=0.

So, in this case b=0, but not a or c.

so, aRc is not true.

Thus, R is not transitive.

Hence, the relation R is symmetric but not reflecive and transitive. It is not an equivalence relation.

Good Luck

Comments (1)

Siddhant Zine

11th Nov, 2020

Sir in question I asked ab is not equal to zero .. anyway thanks for ans

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