Logic and Proof Techniques

1 Propositional Logic
1.1 Propositions and Logical Connectives
1.2 Truth Tables
1.3 Logical Equivalences
1.4 Validity of Arguments
2 Predicate Logic
2.1 Predicates
2.2 Quantifiers
2.3 Negating Quantifiers
2.4 Uniqueness Quantifier
3 Proof Techniques
3.1 Direct Proof
3.2 Proof by Contrapositive
3.3 Proof by Contradiction
3.4 Proof by Cases
3.5 Existence Proofs
3.6 Uniqueness Proofs
3.7 Mathematical Induction
3.8 Strong Induction
3.9 Well-Ordering Principle