First, make a truth table for the relevant statements. (You might want to complete the truth table on paper so you can make columns for intermediate steps; just record the final columns here.) P QR P → (QV R) -(P → Q) TTT TTF TFT TFF FTT F T F FFT FF Is the deduction rule valid? O A. No, because the columns for the two premises are not identical. O B. Yes, because there is a row in which both premises are true. O C. Yes, in every row where both premises are true, the conclusion is also true. O D. No, because the statements are not always true. O E. Impossible to determine without more information.

An argument is expressed in English below. Catalina is sleepy or Catalina is not shocked. Catalina is excited. : Catalina is excited or Catalina is sleepy. Variable names are assigned to each English phrase as follows: •p: Catalina is excited •q: Catalina is shocked •r: Catalina is sleepy What is the form of the argument? Pick Pick v : Pick v

Complete the truth table for the statement ~S → R. S R -S →R T ? v F ? v F ? v F F ? v

Use the statements and truth table to determine which statements are equivalent. p: It is a university. q: It offers a degree in electrical engineering. pqpqpq ~p → ~qqp ~q→ ~p TT FL וד F T T T T TF F T F T T F FT T FL T F FL T FF T T T T T T If it offers a degree in electrical engineering, then it is a university. If it is a university, then it offers a degree in electrical engineering. If it offers a degree in electrical engineering, then it is a university. It is a university, and it offers a degree in electrical engineering. If it offers a degree in electrical engineering, then it is a university. If it is not a university, then it does not offer a degree in electrical engineering. If it is a university, then it does not offer a degree in electrical engineering. It is a university, or it offers a degree in electrical engineering.