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Week 2 Notes

by: Taysha Tutt
Taysha Tutt
GPA 3.65
John Burris

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About this Document

These notes detail contradictions, Tautological Equivalencies, DeMorgan’s Law and any other material we covered in class for week 2.
John Burris
Class Notes
25 ?





Popular in Computer Information Systems

This 5 page Class Notes was uploaded by Taysha Tutt on Saturday August 29, 2015. The Class Notes belongs to CMPS 257 at Southeastern Louisiana University taught by John Burris in Fall 2015. Since its upload, it has received 37 views. For similar materials see DISCRETE STRUCTURE in Computer Information Systems at Southeastern Louisiana University.

Similar to CMPS 257 at SELU

Popular in Computer Information Systems


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Date Created: 08/29/15
What have we learned 1 What are statements 2 Truth Tables Number of Rows 3 Connevtives 4Usefuness Basic Truth Table A B C A gt B A gt BquotC T T T T T T T F T F T F T F F T F F F F F T T T T F T F T F F F T T T F F F F F ABgtltgtBgtA A B AgtB BgtA ABgtltgtBgtA T T T T T T F F T F F T T F F F F T T T A v A gt BAB A Contradiction A A A v A BAB A v A gt BAB 39l39l39l39l I I 39I39I l I39I l I Inn l I39I 39I39I l l 39l39l39l39l39l39l39l39l 39l39l39l39l39l39l39l39l When you have a column that is always false it is a contradiction It is equal to zero O AgtBltgtB gtA A B A B A gtB B gtA AgtBltgtB gtA T T F F T T T T F F T F F T F T T F T T T F F T T T T T TAUTOLOGY 1 Always True DeMorgan s Law AAB ltgt A vB AvB ltgt A AB Tautological Equivalancy Always true 1 TAUTOLOGICAL STATEMENT realworld Example A A B if outflowgtinflowampampoutfowgtinflowampamppressure lt1000 do something else do something AAA B A B AAB AAB AA AAB nn I I n n I 39I39I39I39I39I39I I 39I39I 39l39l39l39l I39l39l if outflowgtinflowampamppressure lt1000 do something else do something TAUTOLOGICAL EQUIVALENCES use these all the time to simplifysolve wffs 1 A AVBltgtBVA 1 B AABltgtB A Communitive Property 2AAvaCltgtAvBvC ZBAABACltgtAABAC Associative Property it doesnt matter if what is on the left or right goes first 3AAvBACltgtAvBAAvC 3BAABvCltgtAABvA C Distributive 4A AVOltgtA 4B AA1ltgtA Identity 5AAvA ltgt 1 SBAquotA ltgtO 6AAquotB ltgt A vB GBAvB ltgt A AB A A AVA Ch1 Se2 Propositional Logic combine related statements Things need a relationship its not about always being true Can we draw a conclusion from a set of propositions P1 A P2 A APn gt G Propositionshypotheses Conclusion If the Ps can reachdeduce Q then we have a VALID ARGUMENT Below is not a valid arguement even though it adds up it doesnt make sense P1George Washington was the first president of the United States P2Thomas Jefferson wrote the Declaration of lndependance QTherefore there are 24 hours in a day P1 AP2 gtQ TgtT T


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