In each of the following exercises, verify the given statement carefully, proceeding step by step. Validate each step that involves an inequality by using some statement found in this section.
Suppose that a, b, c ∈ R and a ≤ b.
a) Prove that a + c ≤ b + c.
b) If c ≥ 0, prove that a · c ≤ b · c.
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