Suppose two serial activities A and B are the only activities in a precedence diagramming network. Activity A precedes activity B. There is an SS restriction of 4 time units and an FF restriction of 3 time units between A and B.

a. Determine the mathematical relationship between the duration of \(A\left(t_{A}\right)\) and the duration of \(B\left(t_{B}\right)\).

b. Verify your response to part (a) by considering the following alternate cases: 

Case 1: \(t_{A}=0\)

Case 2: \(0

Case 3: \(1

Case 4: \(t_{A}=4\)

Case 5: \(t_{A}>4\)