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Question
Give an example of a relation which is transitive but neither reflexive nor symmetric?
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Solution
Relation R = {(x, y), : x > y}
We know that x > x is false.
∴ R is not reflexive.
If x > y does not imply y > x.
∴ R is not symmetric.
If x > y, y > z implies x > z.
∴ R is transitive.
Thus, R is transitive but neither reflexive nor symmetric.
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