Predicate Logic Question 01 p (X,Y) is a predicate that returns True if X Y, where X and Y are two primes False otherwise. a What is a possible domain for X and Y? b. Find a ground atomic formula for p (X, Y) when X 17 c. Find a ground atomic formula for p (X, Y) when Y 2. d. Find a ground atomic formula for p (X, Y) when Y 3. Answer: a X and Y are positive integers b. p (17, 19) p (17 23) c. No possible answer d. p (2, 3) Question 02: Prove that Vx-POx) 3x P(x) You will find the proof in file s2 3.pdf at pg 52 Question 03: A propositional function (or a predicate) p (x) is given by x2 9 and the universe of discourse (or domain) is 13, 4, 5, 6 Find a counter example to prove that Vx p(x) is an invalid Statement b Find an evidence to prove that 3x p(x) is a valid statement Answer: a If x 3 then p (x) is false b If x 4, p (x) is true