How do I prove the following statements: (a) For all a, b, c ∈ Z, if a < b, then a + c < b + c. (b) For all integers a, b, if 0 < a and a < b, then a^2 a. ● (O2) For all a, b ∈ Z, if 0 < a and 0 < b, then 0 < a + b. ● (O3) For all a, b ∈ Z, if 0 < a and 0 < b, then 0 < a ⋅ b. ● (O4) for all a, b ∈ Z, a < b exactly when 0 < b − a.

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