Discrete Structures Lecture 10 Segment

Basic terminology pertaining to proofs 00:19 Definition: proof & theorem 02:07 Definition: lemma 02:58 Definition: corollary 03:22 ... Proof technique: Trivial proof Prove p → q by proving that q is always true. Basic number theory terminology 00:50 definition: even integer 01:36 definition: odd integer 01:51 definition: perfect square 02:29 ... Proof technique: Universal generalization 00:00 Definition: arbitrary element of the domain 01:13 Proof of theorem in previous ... Proof technique: Direct proof for quantified conditionals Prove ∀x (P(x) → Q(x)) by combining a universal generalization proof ... Proof technique: Direct proof Prove p → q by proving that, assuming p is true, q must also be true.

Proof technique: Vacuous proof Prove p → q by proving that p is always false. Proving the same set equality as in the previous video using two other proof techniques, namely: + proof by equational reasoning ... Discrete Math - Math 2030-850 from Rosen's " 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. Nested quantifiers The order of the quantifiers (sometimes) matters.

Introduction to counting: Examples of using the sum rule 0:00 4 examples 7:54 Complement rule.