Page 1 of 6 Project 4 1-5 Directions 1 Write on your NAME answer sheet Symbolize the following arguments ONLY with the letters indicated at the end of the argument. I will go to the playoffs if the Rangers win. Either the Rangers win or the Islanders win. The Islanders did not win. Therefore, I will not go to the playoffs. ( P, R, I ) A C PR PR R \\/ I ~ I___ ~P B 2 D RP R /\\ I ~ I___ ~P We will play basketball if and only if we have five players. Unfortunately we only have three players. Therefor we will not play basketball. ( B, P ) A B P C BP ~P ~P ~ B ~B B 3 RP R \\/ I ~ I___ ~P R /\\ I ~ I___ ~P B P T ~ B D BP T ~B He is guilty or the judge declared a mistrial. If the judge declared a mistrial, then he will have a new trial. He will not have a new trial. Therefore he is guilty. (G, M, N ) A G \\/ M C GM NM MN ~ N______ ~ N______ G G B D G /\\ M G \\/ M MN MN ~ N______ ~ N______ G G 1 Page 2 of 6 4 The President vetoed the bill or it was not passed by Congress. Congress will override the veto if the President vetoes the bill. Congress will not override the veto. Therefore the bill was not passed by Congress. ( V, P, O ) A ~ P \\/ ~ C C V \\/ ~ P OP VO ~ O__ ~ O__ ~P ~P B 5 V \\/ ~ P VO ~ O__ P D V \\/ ~ P OV ~ O__ ~P If Pete is correct, then Sam is wrong. It is not the case that Pete is not correct or Sam is wrong. Therefore, Pete is correct. ( P, S ) A SP C PS ~ ( ~ P \\/ ~ S )__ ( P \\/ S )__ P P B SP ~ ( P /\\ S )__ P D PS ~ ( ~ P \\/ S )__ P 6 -10 Determine if the truth value of the indicated statement is: A) True B) False C) Can not be determined. 6 If ~ R is False and ( Q /\\ ~ P ) Then Determine the truth value of 7 If X is False, Then Determine the truth value of ~Y) 8 If 9 If is a premise, ( ~ P ( ~ Q \\/ ~ R ) ) ( ~ C /\\ D ) is a Premise Then Determine the truth value of ~ ( Q R ) and P are premises Then Determine the truth value of ( Y X ) \\/ ( X ( ~ A \\/ D ) ~ ( B D ) ( ~ Q /\\ P ) 2 Page 3 of 6 10 If 11 ( P /\\ S ) \\/ E is FALSE and ~ P W is a premise Then Determine the truth value of W With the argument below assume you tried to use the T-F Indirect Method. ( P /\\ S ) \\/ E ~ E P~ W WE What additional statement would you assume to be a true premise in order to use the T-F Indirect Method based on the Argument above? A B C D W ~E ~ W \\/ E ~(WE) 12-14) Assume you want to use the T-F Conditional Method on the argument below: (AB)C ~ C \\/ W ( ~ B \\/ W ) S ( ~ A /\\ B ) S 12) What additional statement would you assume to be a true premise in order to use the T-F Conditional Strategy method on the argument above? A ~ ( ~ A /\\ B ) B ~ ( ~ A /\\ B ) S C ~C D ( ~ A /\\ B ) 13) By using the T - F Conditional Strategy method what do you find the truth value of the statement ~ C A True B False C Cannot determine 3 Page 4 of 6 By using the T - F Conditional Strategy method what do you find the truth value of the 14) statement W ? A True B False C Cannot determine 15-16) With the argument below you could use the T-F Indirect Method Approach. ~ B \\/ W B /\\ Z (~ W \\/ Z ) A ( ~ P \\/ A ) 15) What additional statement would you assume to be a true premise in order to use the T-F Indirect Method Approach on the statement above? A (~ P \\/ A ) B C D 16) A ~ ( ~ P \\/ A ) ~ P If you rewrote the conclusion by the conditional equivalence, you could have ( P A) as the conclusion. In that case, you might try to use the T - F Conditional Strategy method. What additional statement would you assume to be a true premise in order to use a Conditional Strategy T - F method on the argument above? A B C D ~(P A) P (P A) A 4 Page 5 of 6 17 - 20 Directions: In each of the arguments below an equivalence ( either DeMorgan, Conditional or Contrapositive Equivalence) needs to be used to show the argument to be valid. Which equivalence : Use A) Conditional B) Contrapositive C) DeMorgan Arguments 17 and 19 Arguments 18 and 20 17) Which equivalence could be used on ( ~ R \\/ ~ Q ) in order to more easily show the argument valid with T- F method? ~ P (R /\\ Q ) _~ R \\/ ~ Q P 19) 18) Which equivalence could be used on (~ R P ) in order to more easily show the argument valid with T- F method? ~ P \\/ ~ ( ~ P R ) ~R P ~ ~P Which equivalence could be used 20) Which equivalence could be on ~ (P \\/ R) in order to more easily used on (~ R ~ P ) in order to show the argument valid with T- F more easily show the argument method valid with T- F method? Q (~PR) ~ ( P \\/ R ) ~Q Q ~(PR) ~R~P ~Q 21) Under which condition below is an argument considered invalid? A) Only when the premises are True B) When all the premises are assumed to be True, then the conclusion is also True C) Only when the conclusion is False D) When all the premises are assumed to be True, then the conclusion is also False. 5 Page 6 of 6 2225) Use the T-F method with equivalences (if needed), and the conditional or indirect method (if needed), to show the argument to be Valid or Invalid. The only answer you will be giving is A ) Valid or B) Invalid. Arguments 22 and 24 Arguments 23 and 25 22) ~ ( B /\\ C ) ~ A A \\/ ~ E E /\\ ~ G B \\/ ~ M 23) ~ B ~ A B ( C \\/ D ) ( A /\\ ~ C ) ~ D 24) ( P S) ~T ( ~ S \\/ T) P ~S 25) ( ~ M ~ E) /\\ A ~ ( ~ E /\\ ~ S ) P \\/ ~ M (A~P) S End of Project 4 6