**1. Introduction**

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),

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