Britannica
Sources used in this answer
How are compound propositions formed in propositional logic?
Created from Britannica articles
using AI.
AI can make mistakes, so verify using Britannica articles.
Formal logic
Alfred North Whitehead.
In propositional logic, compound (or molecular) propositions are constructed by joining simple, atomic propositions using logical connectives. These connectives function as operators that take one or more propositions as arguments to form a new, complex proposition.123
The standard logical operators used to form these compounds include:
- Negation (~ or ¬): A monadic operator that reverses the truth value of a single proposition.34
- Conjunction (· or &): A dyadic operator that joins two propositions, asserting both are true.34
- Disjunction (∨): A dyadic operator that asserts at least one of the two propositions is true.34
- Conditional (⊃): A dyadic operator representing "if... then" relationships.34
- Biconditional (≡): A dyadic operator representing "if and only if" relationships.34
Brackets or parentheses are also employed to group these elements, ensuring the logical structure and order of operations are clearly defined. Because these operators are truth-functional, the truth value of the resulting compound proposition is determined entirely by the truth values of its component parts.34