Two sets $A$ and $B$ are considered **equal**, if $A$ is a subset of $B$, and vice versa. Formally:

$$A=B\Longleftrightarrow (A\subseteq B)\wedge (B\subseteq A).$$

The negation of the **equality** of sets is their **inequality** and denoted by $A\neq B.$

- The set of all animals and the set of all whales are not equal since every whale is an animal but not every animal is a whale.
- The set of all whole numbers $a\ge 0 $ equals the set $\mathbb N$ of all natural numbers.
- The sets $\{3,6,7\}$ equals the set $\{7,3,6\}.$

| | | | | created: 2017-08-13 11:44:27 | modified: 2020-05-10 18:35:44 | by: *bookofproofs* | references: [711]

[711] **Mendelson Elliott**: “Theory and Problems of Boolean Algebra and Switching Circuits”, McGraw-Hill Book Company, 1982