These notes follow closely notes originally developed by Alexander Kechris for the course Math 6c at Caltech.
Somewhat informally, a proposition is a statement which is either true or false. Whichever the case, we call this its truth value.
Example 1 “There are infinitely many primes”; “”; and “14 is a square number” are propositions. A statement like “ is odd,” (a “propositional function”) is not a proposition since its truth depends on the value of (but it becomes one when is substituted by a particular number).
Informally still, a propositional connective combines individual propositions into a compound one so that its truth or falsity depends only on the truth or falsity of the components. The most common connectives are:
- Not (negation),
- And (conjunction),
- Or (disjunction),
- Implies (implication),
- Iff (equivalence),