Name (printed):Student ID #:Section # (or TA’s:name and time)CMSC 250 Quiz #3 ANSWERS Wednesday, Feb. 9, 20041. [16 pnts.] For each of the following, tell the translation of that argument using the propositionsgiven. Also, for each of the following identify the ONE rule being applied or tell that it is not oneof those rules listed in your textbook and on the “cheat sheet”. Do not make any assumuptionsabout meaning (in other words, assume “If you pass CMSC250, you will graduate.” is a separateand independant statement from “If you graduated, you passed CMSC250”.Propositions:G = “You graduated.”D = “You passed CMSC250.”C = “You passed CMSC311.”a.If you graduated, you must have passed bothCMSC250 and CMSC311.G → (D ∧ C)You passed both CMSC250 and CMSC311. (D ∧ C)You graduated. GState the name of the rule that was applied here (or none): noneb.You passed CMSC 250. DYou passed CMSC 311. CIf you pass CMSC 250, you will graduate. D → GYou will graduate. GState the name of the rule that was applied here (or none): MPc.You graduated. GYou passed CMSC 250. DIf you graduate, you must have passedCMSC250.G → DState the name of the rule that was applied here (or none): noned.If you graduated, then you must have passedboth CMSC250 and CMSC311.G → (D ∧ C)It’s not the case that you passed bothCMSC250 and CMSC311.∼ (D ∧ C)You did not graduate. ∼ GState the name of the rule that was applied here (or none): MT↓ TURN OVER ↓Prove each of the arguments on the next page using only the rules from Chapter 1 (These are thesame as the rules on the handout attached). Make sure you are using only those rules. For each line,make sure you tell the statement known to be true, the rule used to get that statement, and the linenumbers to which the rule was applied to get that statement.2. [7 pnts.]P1 (R ∨ P ) → (R ∨ Q)P2∼ QP3 ∼ R∼ P# Statement Rule Lines Used1 ∼ R∧ ∼ Q Conj Add P2,P32 ∼ (R ∨ Q) DeMorg 13 ∼ (R ∨ P ) MT P1,24 ∼ R∧ ∼ P DeMorg 35 ∼ P Conj Simp 4OR# Statement Rule Lines Used1 |P Assume2 |R ∨ P Disj Add 13 |R ∨ Q MP P1,24 |R Disj Syll 3,P25 |R∧ ∼ R Conj Add 4,P36 ∼ P Closing Cond Wrld withcontradiction1-53. [7 pnts.]P1 (P ∧ ∼ Q) →∼ PP2 ∼ Q∼ P# Statement Rule Lines Used1 |P Assume2 |P ∧ ∼ Q Conj Add 1,P23 | ∼ P MP 2,P14 |P ∧ ∼ P Conj Add 1,35 ∼ P Closing Cond. Wrld. withContradiction1-4OR# Statement Rule Lines Used1 ∼ (P ∧ ∼ Q)∨ ∼ P Alt Rep of → P12 (∼ P ∨ ∼∼ Q)∨ ∼ P DeMorg 13 (∼ P ∨ ∼ P )∨ ∼∼ Q Comm. and Assoc. 24 ∼ P ∨ ∼∼ Q Idempotent 35 ∼ P ∨ Q Double Neg 46 ∼ P Disj Syll
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