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USEPOSTSC11Assignment2spri. 2 (12 pts 2 x 6) For each of the following propositions use the short-cut method to indicate whether or not it is a tautology. If it is not a tautology then please find a counter-example. You must show your work to get credit ((not imp R) and (P or Q) and not(R)) imp not(P) (not(R) and (R or not and (not(Q) imp P)) imp F (8 pts 4x2) What is the result of each of the following propositions? T, F, R, or not(R) when P = F and Q = T a(P or not(R) imp (R and not(O)) (not(Q) and not(R)) imp (P or R) e (R or notQ) imp (not(P) or not(R)) d(Q imp not(R)) and (not(P) imp notQ)) 4( 16 pts = 4 x 4) For each of the following syllogistic argument forms, use Venn diagrams to determine whether it is valid or not valid If the argument is not valid then please give a counter- example (Venn Diagram). You must show your work to get credit. Answers in separate picture file. No Eare P. Some N are P. Therefore, Some N are not(E) b. All H are Y. All Zare Y. Therefore, no H are Z 5.(18 pts = 6 x 3) For each of the statements below involving these classes W, P and E indicate whether the statement is true (T), false (F), or undetermined (U) by the information given in the diagram by writing the appropriate letter (T, F, U) IMPORTANT: YOU MUST GET THE PICTURE FOR THIS QUESTION in CLASS Some W are not (P) No E are W Some E are P All E are W Some P are W Some P are not(W) USEPOSTSC11Assignment2spri. 2 (12 pts 2 x 6) For each of the following propositions use the short-cut method to indicate whether or not it is a tautology. If it is not a tautology then please find a counter-example. You must show your work to get credit ((not imp R) and (P or Q) and not(R)) imp not(P) (not(R) and (R or not and (not(Q) imp P)) imp F (8 pts 4x2) What is the result of each of the following propositions? T, F, R, or not(R) when P = F and Q = T a(P or not(R) imp (R and not(O)) (not(Q) and not(R)) imp (P or R) e (R or notQ) imp (not(P) or not(R)) d(Q imp not(R)) and (not(P) imp notQ)) 4( 16 pts = 4 x 4) For each of the following syllogistic argument forms, use Venn diagrams to determine whether it is valid or not valid If the argument is not valid then please give a counter- example (Venn Diagram). You must show your work to get credit. Answers in separate picture file. No Eare P. Some N are P. Therefore, Some N are not(E) b. All H are Y. All Zare Y. Therefore, no H are Z 5.(18 pts = 6 x 3) For each of the statements below involving these classes W, P and E indicate whether the statement is true (T), false (F), or undetermined (U) by the information given in the diagram by writing the appropriate letter (T, F, U) IMPORTANT: YOU MUST GET THE PICTURE FOR THIS QUESTION in CLASS Some W are not (P) No E are W Some E are P All E are W Some P are W Some P are not(W)
