(a) Suppose there exists a Turing Machine M that decides LHALT. Using M, design a Turing Machine M' such that for any Turing Machine T, M'((T)) halts if and only if M((T), (T)) rejects. Hint: A Turing Machine can deliberately loop indefinitely. (b) Design an input x for M' that creates paradoxical behavior, and conclude that LHALT is undecidable. (a) Suppose there exists a Turing Machine M that decides LHALT. Using M, design a Turing Machine M' such that for any Turing Machine T, M'((T)) halts if and only if M((T), (T)) rejects. Hint: A Turing Machine can deliberately loop indefinitely. (b) Design an input x for M' that creates paradoxical behavior, and conclude that LHALT is undecidable