Give an example of a Turing Machine that accepts, but doesn't recognize the language $A=\{ 0, 11 \} \subseteq \{0,1\}*$

Question

I'm not sure what "accepts, but doesn't recognize" mean. Does it mean it's not supposed to work with that language, but still accepts?

I also don't understand the notation. What does $A=\{ 0, 11 \} \subseteq \{0,1\}*$ mean? That A is all the possible combinations of 0 and 11?

How do I solve?

Answer 1

According to https://www.cc.gatech.edu/~rpeng/CS4510_F18/Nov12Reductions.pdf:

"Recall that a language L is Turing recognizable if there is a Turing machine that accepts exactly the words in L, but can either reject or loop indefinitely on an input that’s not in L."

So just construct a TM that accepts 0, 11, and some other string, but rejects everything else.

{0, 11} is a subset of {0,1}* because {0,1}* means the set of all 0-1 strings.