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In the following, directly cite any and all properties of the real numbers that are used...

In the following, directly cite any and all properties of the real numbers that are used in your solutions.

(a) Prove or disprove: for all nonzero a ∈ R, there exists a unique a−1 ∈ R such that aa−1 = 1. (Note: M4 only gives existence of a−1, not uniqueness).

(b) Prove or disprove: for all a, b, c, d ∈ R , if a ≤ b and c ≤ d, then ac ≤ bd.

(c) Prove or disprove: ||a| − |b|| ≤ |a − b| for all a, b ∈ R

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