Exercise 1 : [3 marks] Let the proposition p be it is sunny" and q be I go to park. Write the following propositions using p and q: 1. If it is sunny, I go to park. 2. If I do not go to park, it is not sunny. 3. I go to park if and only if it is sunny. Exercise 2: [2 marks] We want to show that p ^ ( p V q) =p ^ q. Using the laws for the left side of this equivalence yields. Exercise 3: [3 marks] Prove that (p ^ q) p is a tautology without using a truth table. Exercise 4: [2 marks] Prove the following using laws of logic: a. p 1 (p V 9) =p. b. (p 19) V p=p. c. 7(1219) (p V q) = p. d. (p1q) = (p 79)