Discrete Structures Lecture 4 Segment

Media Summary: Bubble sort algorithm 0:00 Bubble sort algorithm to sort a finite sequence Laws of propositional logic (i.e., list of useful logical equivalences) 0:00 Commutativity laws 3:14 De Morgan's laws An exhaustive proof is a special case of proof by cases.

Discrete Structures Lecture 4 Segment - Detailed Analysis & Overview

Bubble sort algorithm 0:00 Bubble sort algorithm to sort a finite sequence Laws of propositional logic (i.e., list of useful logical equivalences) 0:00 Commutativity laws 3:14 De Morgan's laws An exhaustive proof is a special case of proof by cases. Second example of using mathematical induction to prove the correctness of a closed-form guess. 0:00 Definition of the "resolution" inference rule 1:43 CS applications of resolution 2:26 The disjunctive syllogism is a special case ... Proof technique: Vacuous proof Prove p → q by proving that p is always false.

Cartesian product 0:00 Definition: n-tuple 1:18 Definition: pair 2:44 Definition: Cartesian product 8:20 Definition: relation 10:01 ... Other useful logical equivalences + equational reasoning 0:00 Conditional equivalence (i.e., replacing implication with ... 0:00 Five examples of English sentences translated into predicate logic 7:47 Three examples of predicate logic expressions ... Comparison of proof techniques for a theorem of the form p → q 00:00 Direct proof versus indirect proof (contraposition or ... Predicate logic 0:00 Formalizing the Flipper argument 10:35 The need for quantification. Another fully worked out example of equational reasoning In this video we prove the validity of the argument that we formalized in ...

... let's discuss some direct applications of it for example let's compute the expansion of 3x minus 2y raised to the power Increasing / decreasing (numerical) functions 0:00 Definition: increasing function 3:03 Definition: strictly increasing function