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# Intro Discrete Math CS CS 2050

GPA 3.81

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This 0 page Class Notes was uploaded by Alayna Veum on Monday November 2, 2015. The Class Notes belongs to CS 2050 at Georgia Institute of Technology - Main Campus taught by Monica Sweat in Fall. Since its upload, it has received 14 views. For similar materials see /class/234015/cs-2050-georgia-institute-of-technology-main-campus in ComputerScienence at Georgia Institute of Technology - Main Campus.

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Date Created: 11/02/15

Copyught 2011 All ugth xesexved Duplication andox usage fox puxposes of any kmd without pexmission is stnctly madden Propositions 5 1A125174gt7386 a The proposition is true b The proposition is false c The statement is not a proposition 5 2i 4216V639 a The proposition is true b The proposition is false c The statement is not a proposition 5 3i 33 27 912786 a The proposition is true b The proposition is false c The statement is not a proposition E g i 12994gt223V224 a The proposition is true b The proposition is false c The statement is not a proposition Equivalencies 5 5i 31Pz A E Vz Pz A a The equivalency is true b The equivalency is false 5 6 quEnPVq a The equivalency is true b The equivalency is false Copyught 2011 All gm xesexved Duplication andox usage fox puxposes of any kmd Without pexmission is smcuy madden Showing Equivalency via Truth Table 5 7 Provide a complete truth table to show that the following statement is true You are required to complete the entire truth table showing a column for every small step It must have 4 complete rowsl Be sure to indicate Why the truth table shows that these two statements are logically equivalent nth1Epan Page 2 Copyught 2011 All gm xesexved Duplication andox usage fox puxposes of any kmd without pexmxssxon is stnctly madden Rules of Inference for Your Reference p Modus ponens p H q g Modus tollens p H q p P 4gt 1 Hypothetical syllogism L 4 7 p r p V q Disjunctive syllogism p Addition 2qu p A q Simpli cation p Conjunction pAq p V 4 Resolution p V 7 2qu Page 3 Copyughb 2011 All ugth xesexved Duplication andox usage fox puxposes of any kmd without pexmxssxon is stnctly madden Rules of Inference 10 8 Using rules of inference show that the following hypotheses do conclude With 8 a p V L b 39r H p cl 7 a 3 di q Give the reason for each step as you show that s is concluded Each reason should be the name of a rule of inference and include Which numbered steps are being used Do not use a truth table A solution using a truth table Will receive no credit For example a reason for a step might be Modus tollens using step 1 and step 6 STEP REASON 1 p V q hypothesis 2 r 4gt p hypothesis 3 7 a s hypothesis 4 g hypothesis Page 4 Copyught 2011 All gm xesexved Duplication andox usage fox puxposes of any kmd without pexmission is stnctly madden 9i Translating English to Propositional Logic You are given the following predicates and domain information variables 111 12 represent students variable y represents a course Cz z is a CS major Tzy z is taking y For each of the problems given write a statement using only the following predicates and variables listed above negation and parentheses You are NOT allowed to use ED 3 H nor anything beyond those expressly allowed 5 a Every course that is not a math course has at least one student that is a Freshman CS majori 5 b Every Freshman is taking at least one nonmath course 5 c Exactly 2 Freshmen are CS majorsi Nested Quanti ers 5 10 Rewrite the following statement so that all negation symbols immediately precede predicatesi You are not required to show the intermediate steps Vx3yPz y A I f y V QltIv Page 5 Copyughb 2011 All gm xesexved Duplication andox usage fox puxposes of any kmd without pexmxssxon is stnctly madden Proofs 15 11 Direct Proof Using the de nitions of even integer and odd integer give a direct proof that this statement is true for all integers n If I is even and y is odd then I y is odd I y 6 Z Your answer should be in the form of two columns one for statements and one for reasons If you introduce any new variables you must specify their domain STEP REASON Assume z is even and y is odd given 5 12 Disprove the following statement using a counterexample Vnn g n3n 6 Z Page 6

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