Discussion
For a crisp relation R(X, X), iff the pair \(\langle x, y \rangle \in R\) it is also the case that \(\langle y, x \rangle \in R\) for each \(x, y \in X\) for \(x \ne y\), then such a relation is called as a ............ relation.
Answer: B
Such a relation is symmetric.
A relation R on X is symmetric when, for every pair of distinct elements, \(\langle x, y \rangle \in R\) implies \(\langle y, x \rangle \in R\), which is exactly the condition stated.
Reflexive means every element is related to itself. Transitive means \(\langle x, y \rangle\) and \(\langle y, z \rangle\) in R give \(\langle x, z \rangle\) in R. Nontransitive means that transitivity fails for some triple. None of these concerns reversing a pair.
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