Question 1 [2 marks] Prove that p => q E q :> up. Question 2 [2 marks] Prove p /\\ q :> 10 V q. Question 3 [2 marks] Prove p V (up /\\ q) E p V q. Use the Golden Rule and manipulate. Question 4 [2 marks] Prove 1) V q :> p /\\ q E p E q Question 5 [2 marks] Assume that the theorem of the previous question holds (i.e., (p V q 2 p /\\ q) E p E q). Use the duality theorem to prove -|((p V q) V (p /\\ q)) E p s q. You may use that psi qi=s