Which of the following statements are always true? Justify

Chapter 3, Problem 3.32

(choose chapter or problem)

Which of the following statements are always true? Justify your answers.

(a) If A + B = C, then \(AD^\prime  + BD^\prime  = CD^\prime \)

(b) If \(A^\prime B + A^\prime C = A^\prime D\), then B + C = D

(c) If A + B = C, then A + B + D = C + D

(d) If A + B + C = C + D, then A + B = D

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