# Category:Set Equality

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This category contains results about **Set Equality**.

Definitions specific to this category can be found in **Definitions/Set Equality**.

Let $S$ and $T$ be sets.

### Definition 1

$S$ and $T$ are equal if and only if they have the same elements:

- $S = T \iff \paren {\forall x: x \in S \iff x \in T}$

### Definition 2

$S$ and $T$ are equal if and only if both:

- $S$ is a subset of $T$

and

- $T$ is a subset of $S$

## Pages in category "Set Equality"

The following 5 pages are in this category, out of 5 total.