E: a) Write each of the following three statements in symbolic form and determine which pairs are logically equivalent. Justify your answer If it walks like a duck and it talks like a duck, then it is a duck." Either it does not walk like a duck or it does not talk like a duck, or it is a duck." "If it does not walk like a duck and it does not talk like a duck, then it is not a duck. b) Write the negation of each of the following two statement For all real numbers x and y with x There exists an intezer n such that n is composite and n is not even and n s 2 y, there exists an integer n such that x n y II. Write in symbolic form (a). Use the rules of inferences to prove if the argument is valid or invalid for both (a) and (b). Show the steps to get the full credits If Dominic goes to the racetrack, then Helen will get mad. If Ralph plays cards all night. then Carmela will get mad. If either Helen or Carmela gets mad, then Veronica (their attorney) will be notified. Veronica has not heard from either of these two clients. Consequently, Dominic didn't make it to the racetrack and Ralph didn't play cards all night. b. c. Draw a Circuit for the following input/output table: Inpurs OutpITS