Answer
See explanations.
Work Step by Step
a. Step 1. If $a\geq b$, we have $|a-b|=a-b$ and max{a,b}=$\frac{a+b}{2}+\frac{a-b}{2}=a$
Step 2. If $a\leq b$, we have $|a-b|=b-a$ and max{a,b}=$\frac{a+b}{2}+\frac{b-a}{2}=b$
b. Step 1. Define min{a,b}=$\frac{a+b}{2}-\frac{|a-b|}{2}$.
Step 2. If $a\geq b$, we have $|a-b|=a-b$ and min{a,b}=$\frac{a+b}{2}-\frac{a-b}{2}=b$
Step 3. If $a\leq b$, we have $|a-b|=b-a$ and min{a,b}=$\frac{a+b}{2}-\frac{b-a}{2}=a$
