Prove, using a reduction argument such as given in Section 17.3.2, that the problem of determining whether there is some input on which two arbitrary programs will both halt is unsolvable. Prove,...

Prove, using a reduction argument such as given in Section 17.3.2, that the problem of determining whether there is some input on which two arbitrary programs will both halt is unsolvable.

Prove, using a reduction argument such as given in Section 17.3.2, that the problem of determining whether an arbitrary program halts on all inputs is unsolvable.