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.
\(
\neg (P ∧ Q) ⇔ \neg P ∨ \neg Q \\
\neg (P ∨ Q) ⇔ \neg P ∧ \neg Q
\)