Question: How to do with piecewise

I have 2 question

1. the first question

how to simple expression below

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is new form 


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2. the second question

plz, explain for me why

> a := piecewise(t <= 100., 0., t < 100 and t <= 160, 1, 160. < t, 0.):

b := piecewise(t <= 100., 0., t < 100 and t <= 160, 2, 160. < t, 0.):

> simplify(a - b);

have result is 0

 

 

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