I'm sorry to say, but this wording is vague, and could be replaced by: "show that there exists an infinite language L such that (a) does not hold."

The animals and elephants, for that matter, are not vague.

But never mind, thanks.

Not all animals are elephants.

In (a) you are asked to show that all elephants are animals (= That all infinite languages in RE have property P)

In (b) you are asked to show that some animals are not elephants (= That not all infinite languages have property P).

I don't see how is that vague.

]]>Thanks a lot! ]]>

(a) states: for all infinite L in RE: exists sub language of L, L' s.t L' is in R

what you are asked to disprove in (b) is:

for all infinite L in U: exists sub language of L, L' s.t L' is in R

or prove the opposite:

exists an infinite L in U s.t. for every sub language of L, L': L' is not in R

since this is not true for languages in RE (as proved in (a)), you should prove:

exists an infinite L in U\RE s.t. for every sub language of L, L': L' is not in R

]]>And still, proof for an infinite language L in general contains cases where L belongs to RE. ]]>

I've just wanted to clear it up: Suppose we do prove claim (a) for the RE class, and then prove that for every infinite language L in general the claim in (a) is not true.

Isn't (b) a little bit stronger then (a)? If we prove that (a) is not true for any language L, then it is not true for a language L in RE…?

Can someone settle this…? where did I get it wrong?

Thank you!

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