Foundations: Logic and Proofs

Identify and use logical connectives (and, or, not, implies, iff) to form compound statements.

Determine the truth value of compound propositions using truth tables.

Negate statements involving universal and existential quantifiers.

Construct a direct proof for a simple conditional statement about properties of integers.

Construct a proof by contrapositive for a simple conditional statement.

Construct a proof by contradiction.

Prove statements using the principle of mathematical induction.

Prove statements using the principle of strong induction.