For any activity with duration D, the standard CPM timing relations are: EF = ES + D, LS = LF - D, LF = LS + D, and D = EF - ES—hence, all the listed relations hold good.

Introduction / Context:Forward and backward pass computations in CPM produce earliest and latest times. Consistency relations link these times to activity duration D.

Given Data / Assumptions:

• Activity duration = D.
• Earliest start/finish: ES, EF; Latest start/finish: LS, LF.

Concept / Approach:By definition, EF equals ES plus D. Similarly, during the backward pass, LS equals LF minus D. Rearranging gives LF = LS + D and D = EF - ES. These equalities are fundamental identities used in CPM calculations and float derivations.

Step-by-Step Solution:1) Forward pass: EF = ES + D.2) Backward pass: LS = LF - D.3) Rearrangement: LF = LS + D.4) From forward pass: D = EF - ES.

Verification / Alternative check:Test with a sample duration D = 5 units: if ES = 10, then EF = 15; if LF = 22, then LS = 17; all identities check out numerically.

Why Other Options Are Wrong:

• Each of A–D is correct; hence the comprehensive selection is required.

Common Pitfalls:

• Mixing earliest and latest columns when computing floats.
• Incorrectly applying calendars or lags without adjusting formulas.

Final Answer:all the above.