Give an example of a relation which is, Reflexive and symmetric b… - Vidyadip

Question

Give an example of a relation which is,
Reflexive and symmetric but not transitive.

✓

Answer

Let A = {4, 6, 8} Define a relation R on A as: A = {(4, 4), (6, 6), (8, 8), (4, 6), (6, 4), (6, 8), (8, 6)}Relation R is reflexive since for every $\text{a}\in\text{A},\ (\text{a, a})\in\text{R}$ i.e., (4, 4), (6, 6), (8, 8) $\in\text{R}$
Relation R is symmetric since $(\text{a, b})\in\text{R}\Rightarrow\ (\text{b, a})\in\text{R}$ for all $\text{a, b}\in\text{R.}$
Relation R is not transitive since (4, 6), (6, 8) $\in\text{R,}$ but $(4,8)\notin\text{R.}$
Hence, relation R is reflexive and symmetric but not transitive.

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