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x^(2)=xy is a relation which is...

`x^(2)=xy` is a relation which is

A

symmetric

B

reflexive and transitive

C

transitive

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Reflexive `xRx`
since, `x^(2)=x*x`
So, R is reflexive
Symmetric `x^(2)=xy cancel(implies)y^(2)=xy`
So, R is not symmetric. E.g. 0R2 but 2R0.
Transitive `xRy impliesx^(2)=xy`
and `yRzimpliesy^(2)=yz`
Now, `x^(2)y^(2)=xy^(2)z`
`impliesx^(2)=xyimpliesxRz`
So, it is transitive.
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