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.
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