Conjunction

Conjunction

The conjunction of two propositions P and Q is the proposition that is true when the propositions P and Q are both true, and false if one of the two propositions is false.

Symbol

The logical conjunction of the propositions P and Q is noted as “P ∧ Q” and is read as: “P or Q”.

Properties

• The truth table of the conjunction is:
 P Q P ∧ Q 1 1 1 1 0 0 0 1 0 0 0 0

In which 1 = true and 0 = false.

• Logical conjunctions and logical disjunctions are connected by the De Morgan’s laws.
$$\neg (P ∧ Q) ⇔ \neg P ∨ \neg Q \\ \neg (P ∨ Q) ⇔ \neg P ∧ \neg Q$$