onsider the following computational problems ZTM={MMisaTuringmachineand0L(M)} ) (9 points) Complete the proof that ATM mapping-reduces to ZTM by filling in the appropriate blanks. Proof: Consider the computable function F: defined by: F= "On input x : - If x=M,w for some TM M then output const out - Otherwise, x=M,w. - Construct a Turing Machine X= "on input y : - If y has length greater than 1 , reject. - If y=0, reject. - If x=0,runM on w - If M accepts w then accept, if M rejects w then reject. Output Explain why F is a mapping reduction from ATM to ZTM by filling in the following blanks: Fill in the blanks about machine X depending on machine M : - if M,wATM, then L(X)= F(M,w)= - if M,w/ATM, then L(X)= - F(M,w)= F(M,w)_ or /ZTM - if x=M,w, then F(x)= - F(x) _\& /ZTM (6 points) Design a mapping-reduction function from ZTM to ATM. (No Justification necessary.)