About computable sets


Let TOT be the set of all Turing Machines that halt on all inputs. Find a computable set B of ordered triples such that:

TOT = {e : ($ \forall$ x)($ \exists$ y)[(e, x, y) $ \in$ B]

This definition means that TOT is a set of all Turing machines e such that they halt on all inputs. The “for all” x denotes all inputs to that machine, and “there exists” a y denotes that e halts under y steps. x consists of 0s and 1s, y and e are Natural numbers too ( e denotes Turing machine $ T_e$ if we were to number all our turing machines)

I had a very fundamental doubt because of which I couldn’t progress at all. How do we construct B?

Thank you in advance.