To show that a TMFbehaves like a reduction fromAtoB, you need to show thatw∈Aif and only if f(w)∈B where f(w) is the output of running F on input w.

To Show that the TMF below is a reduction from ATM to EQTM

F="On input〈M, w〉where M is a TM and w is a string:
1.Construct a TM M1 as follows:
M1="On input x
1.accept"
2.Construct a TM M2as follows:
M1="On inputx
1.Run M on input w
2.If Maccepts w, accept.
If M rejects w, reject."
3.Output〈M1, M2=