# Right zero element

THEOREM

False is a right zero element of conjunction.

$$P \wedge \bot \dashv\vdash \bot$$

Proof available

THEOREM

Zero is a right zero element of natural number multiplication.

$$\forall x \in \mathbb{N} : x * 0 = 0$$

Proof available

THEOREM

True is a right zero element of disjunction.

$$P \vee \top \dashv\vdash \top$$

Proof available

THEOREM

The universal set is a right zero element of union.

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

Proof available

LEMMA    $$A \times \emptyset = \emptyset$$

Proof unavailable

THEOREM

The empty set is a right zero element of intersection.

$$A \cap \emptyset = \emptyset$$

Proof available