Preposition Logic and Problems – III

In this article , you will find common laws for preposition logic. These are very helpful in solving problems like simplifying a complex prepositional statement into a simple one. They also form the basis for arguments which you will learn in future lessons.

Identity Laws  (1)

$latex p \wedge T \equiv p$

$latex p \vee F \equiv p$

Domination Laws (2)

$latex p \vee T \equiv T$

$latex p \wedge F \equiv F$

Idempotent Laws (3)

$latex p \vee p \equiv p$

$latex p \wedge p \equiv p$

Double Negation Law (4)

$latex \neg(\neg p) \equiv p$

Commutative Laws (5)

$latex p \vee q \equiv q \vee p$

$latex p \wedge q \equiv q \wedge p$

Associative Laws (6)

$latex (p \vee q) \vee r \equiv p \vee (q \vee r)$

$latex (p \vee q) \vee r \equiv p \vee (q \vee r)$

Distributive Laws (7)

$latex p \vee (q \wedge r) \equiv (p \vee q) \wedge (p \vee r)$

$latex p \wedge (q \vee r) \equiv (p \wedge q) \vee (p \wedge r)$

De Morgan’s Laws (8)

$latex \neg( p \wedge q) \equiv \neg p \vee \neg q$

$latex \neg( p \vee q) \equiv \neg p \wedge \neg q$

Absorption Laws (9)

$latex p \vee (p \wedge q) \equiv p$

$latex p \wedge (p \vee q) \equiv p$

Negation Laws (10)

$latex p \vee \neg p \equiv T$

$latex p \wedge \neg p \equiv F$