Answer the following question in detail please.

Argue whether each of the following statement is True or False. Give a short, high-level proof if the statement is True and a counter-example if the statement is False. Assume that ={0,1} and that A and B are languages over for each of the statements. (a) If A is nonregular, then there exists a nonregular language B such that AB is finite. (b) If A is nonregular, then there exists a nonregular language B such that AB is infinite. (c) If A is infinite, there must exist a language BA that is nonregular. (d) If A is nonregular, B is regular, and AB=, then AB is nonregular