Please help me answer these 7 assignment questions, I need help #DiscretreMath #Help

Answer the following: /l point/ Suppose that the domain of the propositional function P(x) consists of the integers-Z-L 1, and 2. Write out each of these propositions using disjunctions, conjunctions, and negations. l) 2) 1.5 points Use a direct proof to show that the product of two odd numbers is odd. 3) [1.5 points a) Write the following in standard argument form: if Vx(P(x) (Q0x)) and Vx((-P(x) A Q(x) Rx)) are true, then Vx(-R(x)Px)) is also true, where the domains of all quantifiers are the same. b) Using rules of inference, construct a valid argument to prove that the above conclusion in Q2(b)) actually follows from the given premises. (Hint: use the following table.) Reasoning Premise Step Statement 1. Vx(P(x) V (Q(x)) 3. ) (1.5points) Use a table to express the values of the Boolean function: F(x, y,z) yz) 0 01 010 [1.5 points) For the function Fay. ) in Question 4, show that Fd(x, y, z) = identities 5) using Boolean 6) [1.5 points] Using Boolean identities find the sum-of-products expansion of the Boolean function: F(x, y, z) (F + x)z. Show the reasoning at each step of your solution. 7) [L.5 points] Using a truth table and directly from function values, find the sum-of-products expansion of the Boolean function: F(x, y, z) = + x)2. 101