discrete structures

Problem Set 1 Propositional Logic (40 pts) (a) Let j,s, and k denote the propositions that Jasmine, Samir, and Kanti attend, respectively. Express the given conditions using logical connectives. (6 pts) (1) If Jasmine attends, then Samir should not attend. (2) If Samir attends, then Kanti should be there. (3) Kanti will not attend unless Jasmine also does. (b) There are rows in the truth table for the compound statement containing propositional variables p,q, and s.(4pts) (c) A logical binary relation is defined by the truth table below. Which one of the following propositional expressions is logically equivalent to pq ? Use a truth table to prove your answer. (10 pts) qq,pq,pq,pq (d) Show that (pq)(pr) and p(qr) are logically equivalent (do not use truth table). (10 pts) (e) Show that (p(pq))q is a tautology (do not use truth table). (10 pts)