Problem 3 (5 * 2 = 10 points) (a) Let HALT'(x) be defined as HALT'(x) HALT(l(x), r(x)). Show that HALT'(x) is not computable. (b) Suppose we claim that P is a program that computes HALT(x,x). Give a counterexample that shows the claim to be false. That is, give an input x for which P gives the wrong answer. Problem 3 (5 * 2 = 10 points) (a) Let HALT'(x) be defined as HALT'(x) HALT(l(x), r(x)). Show that HALT'(x) is not computable. (b) Suppose we claim that P is a program that computes HALT(x,x). Give a counterexample that shows the claim to be false. That is, give an input x for which P gives the wrong