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Give an example of a relation which is transitive but neither reflexive nor symmetric? - Mathematics

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प्रश्न

Give an example of a relation which is transitive but neither reflexive nor symmetric?

योग
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उत्तर

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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अध्याय 1: Relations - Exercise 1.1 [पृष्ठ ११]

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आरडी शर्मा Mathematics [English] Class 12
अध्याय 1 Relations
Exercise 1.1 | Q 14.5 | पृष्ठ ११

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