Question

If $R=\{(x,y):x$ is wife of $y\}$, then $R$ is

• A. reflexive
• B. symmetric
• C. transitive
• D. an equivalence relation

Answer 1

Answer: (C)

Here, $R$ is not reflexive; as $x$ cannot wife of $x,R$ is not symmetric, as if $x$ is wife of $y$, then $y$ is husband (not wife) of $x$ and $R$ is transitive as transitivity is not contradicted in this case. Whenever $(x,y)\in R$, then $(y,z)\notin R$ for any $z$ as if $x$ is wife of $y$, then $y$ is a male and a male cannot be a wife.