Consider the following variant of the Halting problem: Write an algorithm H such that, given the description of an algorithm A that requires one input, H will return 1 if A stops for any input I and H...

Consider the following variant of the Halting problem:

Write an algorithm H such that, given the description of an algorithm A that requires one input, H will return 1 if A stops for

any input I and H will return 0 if there is at least one input I for

which A does not stop.

In other words, the algorithm H should read the description of A and

decide whether it stops for all its possible inputs or there is at least one

input for which A does not stop.

Show that this version of the Halting problem is also undecidable.