2. (a) Show that ((p g) ^ (q r)) (pr) is a tautology using both (i)...

 

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2. (a) Show that ((p g) ^ (q r)) (pr) is a tautology using both (i) a truth table and (ii) a chain of logical equivalences. Note that you may only use logical equivalences from Table 6 (p. 27 of the Rosen textbook) and the other four starred equivalences given in lecture. At each step you should cite the name of the equivalence rule you are using, and please only use one rule per step. Is this compound proposition satisfiable? Why or why not? (b) Show that (pg) r and p (gr) are not logically equivalent. 2. (a) Show that ((p g) ^ (q r)) (pr) is a tautology using both (i) a truth table and (ii) a chain of logical equivalences. Note that you may only use logical equivalences from Table 6 (p. 27 of the Rosen textbook) and the other four starred equivalences given in lecture. At each step you should cite the name of the equivalence rule you are using, and please only use one rule per step. Is this compound proposition satisfiable? Why or why not? (b) Show that (pg) r and p (gr) are not logically equivalent.