Show that LOOP is reducible to Complement of Halting problem LOOP = {&lt;M,w1,w2,w3&gt;: M is a Turing machine that doesn't halt on at least 2 of the wi} 
HPC = {&lt;M,w&gt; : M is a Turing machine that doesn't halt on w}
Show that LOOP is polynomial time Turing reducible to HPC
I am not sure how to begin solving this kind of problem.
Also the question I am trying to solve brings up the definition of A is polynomial reducible 
to B if there is a B-oracle poly time Turing M such that M(x) accepts x iff x is in A.
Any hints or pointers on this ?
My thoughts :
What I understand by reducibility here is that If I have a Turing machine for HPC
Then I can use this turing machine to determine if &lt;M,w1,w2,w3&gt; is in LOOP
And same the other way If I have a turing machine for LOOP then I can use it 
as a determiner for HPC. Is this a correct way to think about it?
This way it becomes simple and probably easier to prove. But not sure if it
is same as the question that is being asked
The question is given you have an oracle machine/black box for HPC can you decide if &lt;M,w1,w2,w3&gt; is in LOOP.
See the wikipedia page on that: https://en.m.wikipedia.org/wiki/Reduction_(recursion_theory)#Turing_reducibility
The proof is very straightforward as you already know.