Describe how a universal turing machine could be used in

Question

Problem

1. Show that the relation ≤ on the set of languages (or on the set of decision problems) is reflexive and transitive. Give an example to show that it is not symmetric.

2. Describe how a universal Turing machine could be used in the proof that SA is recursively enumerable.

3. Show that if L₁ and L₂ are languages over and L₂ is recursively enumerable and L₁ ≤ L₂, then L1 is recursively enumerable.