Question

Let F be a field (a set with operations + and · satisfying the field

axioms). Prove the following statements about F. Use only the field

axioms and facts proved in class, rather than any intuitive assumptions

about properties of addition and multiplication that you are familiar

with. At each step of the proof state exactly which axiom or known

fact you are using.

(a) For any a, b, c ∈ F, c(a + b) = ca + cb.

(b) For any a, b ∈ F, if ab = 0 then either a = 0 or b = 0.

(c) For any a, b, c ∈ F, if ac = bc and c 6= 0 then a = b.​

Answer 1

Answer:

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