# Universal set

## Definition

$$\mathcal{U} = \{x : \top\}$$
THEOREM

The universal set is a left zero element of union.

$$\mathcal{U} \cup A = \mathcal{U}$$

Proof available

THEOREM

The universal set is a right zero element of union.

$$A \cup \mathcal{U} = \mathcal{U}$$

Proof available

THEOREM

Every set is a subset of the universal set.

$$A \subseteq \mathcal{U}$$

Proof available