Context-free Languages 1. Consider the following inductive definition of monomials and of polynomials in the variables a and b. Monomials .a and b are monomials every non-zero numeral is a monomial; . if n is a non-zero numeral and is either a or b, then if mi and m2 are two monomials, so is m m2; nothing else is a monomial n is a monomial Polynomials 0 is a polynomial; every monomial is a polynomial; nothing else is a polynomial over the alphabet-a, b, ,0, 1, 2,3,4,5,6,7,8,9) over the alphabet U {+,-) if pi and p2 are two polynomials, so are p +P2 and p -P2 (a) Write a context-free grammar for the language of monomials in the variables a andb (b) Write a context-free grammar for the language of polynomials in the variables a andb