Discrete Structures Lecture 5 Segment

Limitations of propositional logic Many arguments use propositions that are related to each other: + e.g.: "something is a dolphin" ...

Definitions + predicate = name for a property (or a verb phrase) e.g.: D stands for "is a dolphin" (with no subject) D is NOT a ...

Predicate logic 0:00 Formalizing the Flipper argument 10:35 The need for quantification.

Proof technique: Trivial proof Prove p → q by proving that q is always true.

0:00 Unary predicates 2:57 Binary predicates 4:56 domain of a variable (or universe of discourse) 12:12 ternary predicates 14:29 ...

Insertion sort algorithm 0:00 Insertion sort algorithm to sort a finite sequence 1:04 Sample trace of the insertion sort algorithm.

Mathematical induction: Sample proof #4.

Inductive/recursive definitions of sets.

In this

Proving set equalities using proofs by mutual containment.

Introduction to counting: The inclusion-exclusion principle 0:00 Statement of the principle for two sets 2:19 Examples.

Strong induction: Counter-example, i.e., incorrect proof by strong induction.

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