Left zero element


THEOREM   

False is a left zero element of conjunction.

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

Proof available

THEOREM   

Zero is a left zero element of natural number multiplication.

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

Proof available

THEOREM   

True is a left zero element of disjunction.

$$\top \wedge P \dashv\vdash \top$$

Proof available

THEOREM   

The universal set is a left zero element of union.

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

Proof available

LEMMA    \(\emptyset \times A = \emptyset\)

Proof unavailable

THEOREM   

The empty set is a left zero element of intersection.

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

Proof available