6) Let R be a commutative ring with identity 1 + 0. (a) Let I and J be ideals of R and assume I S J. Show that J is a prime ideal of R if and only if J/I is a prime idcal of R/I. (b) Let P and Q be...

Need help with ideals for abatract algebra please

Extracted text: 6) Let R be a commutative ring with identity 1 + 0. (a) Let I and J be ideals of R and assume I S J. Show that J is a prime ideal of R if and only if J/I is a prime idcal of R/I. (b) Let P and Q be two distinct maximal ideals of R. Show that the quotient ring R/(Pn Q) has exactly two prime ideals.