please help me with this hm as soon as possible .. i want to check my answers

)1yom) Suppose that the domain of the propositional function P(x) consists of the integers-2,-1,0 1, and 2. Write out each of these propositions using disjunctions, conjunctions, and negations. c) Ex-P) d) -p(x) Use a direct proof to show that the product of two odd numbers is odd. (1.5 points/ a) Write the following in standard argument form: if Vx(P(x) V (Q(x)) and vx((-P(x) A Qx))R(x)) are true, then Vx(-R(x) quantifiers are the same 3) P(x)) is also true, where the domains of all 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.) Step Statement Reasoning Premise 1. Vx(P(x) V (Q(x)) 2. | Vx((-p(x) Q(x)) 3. R(x)) | Premise 4) [1.5 points] Use a table to express the values of the Boolean function: F(, y,z)-yz+ (xyz) x l y 0 5 points) For the function Fox.yz) in Question 4, show that Fd (,y,z) FG,,2) using Boolearn identities 6) [.5 points) Using Boolean identities find the sum-of-products expansion of the Boolean function: F(x, y,z) (y +x)z. Show the reasoning at each step of your solution [L5 points] Using a truth table and directly oints] Using a truth table and directly from function values, find the sum-of-products expansion of the Boolean function: F(x,y,z) ( x)z. 1 01 1