find a regular expression and FA that each define L1 ∩ L2

Question

from the following pairs I am trying to find a regular expression and FA that each define L1 ∩ L2...How would I do this ?

L1 is (ab*)* and L2 is b(a+b)*

this is what I have...I am on the right track here or am I completely wrong ?

Answer 1

Hint:

• Each word of $L_1 = (\mathtt{ab}^*)^*$ starts with $\mathtt{a}$ or is empty.
• All words of $L_2 = \mathtt{b}(\mathtt{a}+\mathtt{b})^*$ start with $\mathtt{b}$ and are non-empty.

I hope this helps $\ddot\smile$