Name printed Student ID Section or TA s name and time CMSC 250 Quiz 3 ANSWERS Wednesday Feb 9 2004 1 16 pnts For each of the following tell the translation of that argument using the propositions given Also for each of the following identify the ONE rule being applied or tell that it is not one of those rules listed in your textbook and on the cheat sheet Do not make any assumuptions about meaning in other words assume If you pass CMSC250 you will graduate is a separate and 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 both CMSC250 and CMSC311 You passed both CMSC250 and CMSC311 You graduated G D C D C G State the name of the rule that was applied here or none b You passed CMSC 250 You passed CMSC 311 If you pass CMSC 250 you will graduate You will graduate D C D G G State the name of the rule that was applied here or none c You graduated You passed CMSC 250 If you graduate you must have passed CMSC250 d MP G D G D State the name of the rule that was applied here or none If you graduated then you must have passed both CMSC250 and CMSC311 It s not the case that you passed both CMSC250 and CMSC311 You did not graduate none none G D C D C G State the name of the rule that was applied here or none TURN OVER MT Prove each of the arguments on the next page using only the rules from Chapter 1 These are the same 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 line numbers to which the rule was applied to get that statement 2 7 pnts P1 P2 P3 1 2 3 4 5 OR 1 2 3 4 5 6 R P R Q Q R P Statement R Q R Q R P R P P Rule Conj Add DeMorg MT DeMorg Conj Simp Lines Used P2 P3 1 P1 2 3 4 Statement P R P R Q R R R P Rule Assume Disj Add MP Disj Syll Conj Add Closing Cond Wrld with contradiction Lines Used Statement P P Q P P P P Rule Assume Conj Add MP Conj Add Closing Cond Wrld with Contradiction Lines Used Statement P Q P P Q P P P Q P Q P Q P Rule Alt Rep of DeMorg Comm and Assoc Idempotent Double Neg Disj Syll Lines Used P1 1 2 3 4 5 P2 1 P1 2 3 P2 4 P3 1 5 3 7 pnts P1 P2 1 2 3 4 5 OR 1 2 3 4 5 6 P Q P Q P 1 P2 2 P1 1 3 1 4
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