(a) Let F be any field. Prove that if a b = 0 for some a,...

 

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(a) Let F be any field. Prove that if a b = 0 for some a, b = F, then a = =0 or b = 0. (b) Let S = {ff: RR} be a set of all real-valued functions defined on R under the usual addition and multiplication of functions. Show that the above implication does not hold in S. (a) Let F be any field. Prove that if a b = 0 for some a, b = F, then a = =0 or b = 0. (b) Let S = {ff: RR} be a set of all real-valued functions defined on R under the usual addition and multiplication of functions. Show that the above implication does not hold in S.