Prove this language is or not regular and Exhibit an algorithm Pumping lemma

I’m working on a Computer Science question and need guidance to help me study.

1.Prove that this language is or not regular. If not, use the pumping lemma.

L={a^nb^n: n>=0}∪{a^nb^(n+1):n>=0}∪{a^nb^(n+2);n>=0}

2. Exhibit an algorithm that, given any three regular languages, L; L1; L2

determines whether or not L = L1L2

If you are not clear about the problem, please refer to the word file.

Please use the knowledge chapter 4 and 5 from the e-book