6. ProveL={yy|y∈Σ∗}is not regular.
For a language to being a regular language, we know that if we can build a Finite state automata for any language then it is regular.
FSA has a property to remember pattern, but it does not have any memory to store some thing.
For language , we can easily remember pattern of y but FSM doesn't have memory to store y and compare to some string y' to match y=y'.
Therefore we can't build any FSM for the language L. Hence it is not regular language.
Note : However it can be build using push down automate. But this is beyond this question.
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