Let f: R→ R' be a ring homomorphism of commutative rings R and R'. Show that if the ideal P is a prime ideal of R' and f−¹(P) ‡ R, then the ideal f−¹(P) is a prime ideal of R. [Note: ƒ−¹(P) = {a ≤ R| ƒ(a) = P}]