1. Prove that ((p + q) 1 -q) + np is a tautology without using truth tables. Also, do not give a simple English argument. Prove it by using only the logical equivalences learnt in class (all the equivalences from Table 6 and just the first one from Tables 7 and 8 in Section 1.3). Show all intermediate steps and for each step mention as to what law you are using. (15 Pts.) 2. Prove that pHq is logically equivalent to (p1q) v GPA) using the logical equivalences learnt in class (all the equivalences from Table 6, and just the first one from Tables 7 and 8 Section 1.3). Do not solve it using Truth Tables or by simple English argument. Show all intermediate steps and for each step mention as to what law you are using. (15 Pts.)