Hi I have some questions that I need some help with that are from a past paper, thanks.

b. (3 marks) Is the statement (PAQ) V(P V (PQ)) a tautology, contradiction, or a contingent statement? Give reasons for your answer C. 4 marks) Use that QA is a contradiction, and the laws of logic discussed in lectures to prove that d. 6 marks) Consider the statement i. Express the statement in plain English. ii. Negate the statement, and write the negation using only quantifiers and logical connectives. iiDetermine whether the statement is true or false, giving reasons for your answer. e. (4 marks) Prove by contradiction that v3 is irrational. (6 Marks) Consider the argument: I will go out to the restaurant or go out to the movies. If I go to both the restaurant and movies, I will need my credit card. I went to the movies and I didn't need my credit card. Therefore, I didn't go to the restaurant." Rewrite the argument into logical form, and then use a truth table to check the validity of the argument