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**i) Show that a/b + c/d and an/(bn) + c/d , n is an element of I are equivalent. All denominators are assumed to be nonzero.**

ii) Prove that, in a ring R, m.0 = 0 for each m in R.

ii) Prove that, in a ring R, m.0 = 0 for each m in R.

**i) an/(bn) + c/d = {and + (bn)c}/(bn)d = {and + (b)nc}/(b)nd (I is distributive), Hence, a/(b) + c/d = LHS. RHS = a/b + c/d. Hence LHS ~ RHS #.**

ii) m.0 = m(n - n) where n is in R

Thus m.0 = mn -mn (R is distributive)

Hence m.0 = 0

ii) m.0 = m(n - n) where n is in R

Thus m.0 = mn -mn (R is distributive)

Hence m.0 = 0