True or False (and justify).

a) For each Turing machine M, there is some Turing machine M1 with L(M) = L(M1) and such that M1

never loops (i.e. its computations must accept or reject).

b) For each Turing machine M, there is some Turing machine M2 with L(M) = L(M2) and such that M2 never rejects (i.e. its computations must accept or loop).

c) For each Turing machine M, there is some Turing machine M3 with L(M) = L(M3) and such that M3 never accepts (i.e. its computations must reject or loop).