A compound proposition is a proposition formed by combining two or more simple (atomic) propositions using logical connectives.
A compound proposition is a declarative statement whose truth value depends on the truth values of its component propositions and the logical operators used to combine them.
| Symbol | Name | Meaning | Example |
|---|---|---|---|
| ¬ | NOT (Negation) | Reverses truth value | ¬p |
| ∧ | AND (Conjunction) | True if both are true | p ∧ q |
| ∨ | OR (Disjunction) | True if at least one is true | p ∨ q |
| → | IF–THEN (Implication) | Conditional statement | p → q |
| ↔ | IF AND ONLY IF (Biconditional) | True when both have same value | p ↔ q |
Let:
Then:
p ∧ q“7 is a prime number and 7 is an even number”→ False
p ∨ q“7 is a prime number or 7 is an even number”→ True
¬p“7 is not a prime number”→ False
p → q“If 7 is a prime number, then 7 is an even number”→ False
p ↔ q“7 is a prime number if and only if 7 is an even number”→ False
| p | q | p ∧ q |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | F |
This table shows how the truth value of a compound proposition is determined.