True or False with reasons. Decide whether or not the following statements are true or false. Include a short reason for your answer in the space provided below. (i) If R and S are isomorphic commutative rings, then each ring homomorphism f : R → S is an isomorphism. TRUE or FALSE. (ii) If I and J are ideals in a commutative ring R, then I S J is also an ideal. TRUE or FALSE. (iii) If R is an integral domain, then every unit in R[x] has degree zero. TRUE or FALSE. (iv) If f : R → S is a homomorphism of commutative rings, then S has a subring that is isomorphic to R/ ker f. TRUE or FALSE. (v) If I is a proper ideal in a commutative ring R, then R has a subring that is isomorphic to R/I. TRUE or FALSE