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1. Given the following table, make a PERT diagram, and determine the project time and the critical path. Provide a justification on how you obtain your project time and critical path.
Task Time Preceding Tasks
A 1 None
B 2 A
C 3 A
D 4 B
E 5 B, C
F 2 C
G 2 D, E, F
2. Simplify expression: (B-A) UNION (B INTERSECTION A). Show the detailed, step-by-step, simplification and justification.
3. Simplify expression: ((A-B) BAR) UNION A. Show the detailed, step-by-step, simplification and justification.
Check that N(t) = t/(1 +ct) is a solution of the differential equation dN/dt = N^2/t^2. Treat c as an unspecified constant.
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The trigonometric function to find exact value.
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