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Question

x2=xy is a relation which is:

A
Symmetric
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B
Reflexive
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C
Transitive
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D
All of these
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Solution

The correct option is D All of these
xRxx2=x.x Hence reflexive

xRyx2=xy.x=y yRxy2=xyy=x Hence symmetric

xRy and yRz x2=xyx=y. Also y2=yzy=z

Since x=z,x.x=z.xx2=xzxRz. Hence transitive.

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