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

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