subset inclusion doesn't determine difficulty!
ATM reduces to HALTTM = given a genie for problem X, we could decide problem Y
ATM is a subset of HALTTM
Statement: Σ* reduces to ATM -> Given a decider of ATM, I can build a decider for Σ* -> true
Σ* is decidable: we can build a TM that accepts all possible strings.
A is mapping reducible to B -> there is a computable function f such that for all strings x in Σ*