Mathematical Reasoning: Writing and Proof (PreTeXt Edition)

Theorem 9.1.

Let $A\text{,}$ $B\text{,}$ and $C$ be sets.

1. For each set $A\text{,}$ $A\approx A\text{.}$

2. For all sets $A$ and $B\text{,}$ if $A\approx B\text{,}$ then $B\approx A\text{.}$

3. For all sets $A\text{,}$ $B\text{,}$ and $C\text{,}$ if $A\approx B$ and $B\approx C\text{,}$ then $A\approx C\text{.}$