Question:
A relation $\phi$ from $C$ to $R$ is defined by $x \phi y \Leftrightarrow|x|=y$. Which one is correct?
(a) $(2+3 i) \phi 13$
(b) $3 \phi(-3)$
(c) $(1+i) \phi 2$
(d) $i \phi 1$
Solution:
(d) $i \phi 1$
$\because|2+3 i|=\sqrt{13} \neq 13$
$|3| \neq-3$
$|1+i|=\sqrt{2} \neq 2$
and $|\mathrm{i}|=1$
So, $(i, 1) \in \phi$