We have set $X = \mathbb{C},z_1\sim z_2 \leftrightarrow$ Im $z_1$ $\leq$ Im $z_2$.
How to determine if this relation is:
reflexive
symmetric
antisymmetric
transitive?
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Sign up to join this communityWe have set $X = \mathbb{C},z_1\sim z_2 \leftrightarrow$ Im $z_1$ $\leq$ Im $z_2$.
How to determine if this relation is:
reflexive
symmetric
antisymmetric
transitive?
Use the following definitions:
$z_1\sim z_1$
$z_1\sim z_2 \implies z_2 \sim z_1$ for $z_1\neq z_2$
$z_1\sim z_2 \text{ and }z_1\neq z_2 \implies z_2\not\sim z_1$
$z_1\sim z_2 \text{ and } z_2\sim z_3 \implies z_1 \sim z_3$