Answer TRUE or FALSE for parts a-d. Thank you.

DECTM M) | M is a Turing machine and M is a decider Consider the computable function on specified by the algorithm (Turing machine): F4-"On input , 1. Type check if x = M for some Turing machine M 2. If not, output r. 3. If so, build the new Turing machine M-"On input y 1. Run M on y. If it accepts, loop; if it rejects, accept." 4. Output M")" (a) True or False: For all strings x *, if x then F4(zJe DECTM- (b) True or False: For all strings x *, if x ETM then F, (x) DECrM (c) True or False: For all strings x E *, if x E DECTM then F4(zje ETM (d) True or False: For all strings x *, if x DECTM then F4(x) ETM DECTM M) | M is a Turing machine and M is a decider Consider the computable function on specified by the algorithm (Turing machine): F4-"On input , 1. Type check if x = M for some Turing machine M 2. If not, output r. 3. If so, build the new Turing machine M-"On input y 1. Run M on y. If it accepts, loop; if it rejects, accept." 4. Output M")" (a) True or False: For all strings x *, if x then F4(zJe DECTM- (b) True or False: For all strings x *, if x ETM then F, (x) DECrM (c) True or False: For all strings x E *, if x E DECTM then F4(zje ETM (d) True or False: For all strings x *, if x DECTM then F4(x) ETM