Lecture 2: Propositional Logic

1. Atomic vs Compound Propositions

Atomic Proposition

A single statement with no logical operators.

Examples:

• p: "7 is prime"

• q: "25 is divisible by 2"

Atomic propositions are the inputs to everything else.

Compound Proposition

A statement formed by combining atomic propositions using logical operators.

Examples:

• p∧q: "7 is prime and 25 is divisible by 2"

• p∨q: "7 is prime or 25 is divisible by 2"

On exams, you will be expected to:

• Identify atomic propositions

• Rewrite English statements as compound propositions

2. Logical Operators

Negation (NOT) — ¬p

Negation flips the truth value of a proposition.

Examples:

• p: “The sun rises in the east”

• ¬p: “The sun does not rise in the east”

Important transformation:

• ¬(p∧q) becomes “not (p and q)”
  NOT “(not p) and q”

This distinction matters later with De Morgan’s Laws.

Conjunction (AND) — p∧q

True only if bo....