ANSWER TRUE OR FALSE USING INFORMATION BELOW:

DECtm = { | M is a Turing Machine and M is a decider}

Consider the computable function on * specified by this algorithm:

F,-"On input x, 1, Type check if x = M for some Turing machine M. 2. If not, output x. 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 ., ifaE ETA, then F4(2) E DECTM (b) True or False: For all strings x *, if x ETM then F4(x) DECrM (c) True or False: For all strings x E , if x DECTA, then F4(zJe ETM (d) True or False: For all strings x E , if x DECTM then F4(z) ETM