Problem 3 [15 points] If A and B are languages, define In LATEX, you can produce o by using Idiamond in math mode. Prove that if A and B are regular languages, then A. B is context-free. [Hint: Let M, = (Q1, .61, q1, F1) and M2 = (Q2,.62,Y2, F) be DFAs that recognize A and B, respectively. Construct a PDA M = (Q,,,6.90, F) to recognize A B. You may assume that Q1 n Q2 = . for A and a left regular grammar for B and construct a new CFG for A. B.] Alternatively, you can consider a right regular grammair