False


THEOREM   

False is a left zero element of conjunction.

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

Proof available

THEOREM   

False is a right zero element of conjunction.

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

Proof available

THEOREM   

False is a left identity element of disjunction.

$$\bot \vee P \dashv\vdash P$$

Proof available

THEOREM   

False is a right identity element of disjunction.

$$P \vee \bot \dashv\vdash P$$

Proof available

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