Question: 8. Let / and / be ideals in the ring R. (i) Prove that In J is an ideal in R. (ii) Prove thatI +

8. Let / and / be ideals in the ring R. (i) Prove that In J is an ideal in R. (ii) Prove thatI + J = (a+blac l, be J} is an ideal in R. (iii) Prove that is an ideal in R. (iv) Prove that IJ C I n J. Give an example where IJSInJ. (v) Is {ab | a E I, b E J} an ideal in R? 100%

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