Question

Let $R$ be any relation in the set $A$ of human beings in a town at a particular time.
If $R=\{(x, y): x$ is exactly $7\, cm$ taller than $y\}$, then $R$ is

• A. not symmetric
• B. reflexive
• C. symmetric but not transitive
• D. an equivalence relation

Answer 1

Answer: (A)

Here, $R$ is not reflexive as $x$ is not $7\, cm$ taller than $x$.
$R$ is not symmetric as if $x$ is exactly $7 \, cm$ taller than $y$, then $y$ cannot be $7\, cm$ taller than $x$ and $R$ is not transitive as if $x$ is exactly $7 \, cm$ taller than $y$ and $y$ is exactly $7 \, cm$ taller than $z$, then $x$ is exactly $14\, cm$ taller than $z$.