Q.In a project network, activities P and Q both start at event 1 and both end at event 4; P takes 3 days and Q takes 5 days. A third activity, R, can begin only after P (not after Q) is complete. Explain why the network cannot be drawn with P and Q as two ordinary arrows both running directly from event 1 to event 4, and show how a dummy activity resolves the problem.

Two genuine activities are never allowed to share both the same tail and head event; a dummy activity is inserted to give P its own distinct head event so R can depend on P alone.

Step 1 — Identify the rule being violated. This chapter's construction rules state that no two activities may share both the same tail event and the same head event. If P and Q were both drawn directly from event 1 to event 4, they would violate this rule (two distinct arrows between the identical pair of events) — and more importantly, there would be no way to show that R depends only on P and not on Q, since both P and Q would appear to finish at the exact same event 4, making them look interchangeable as R's predecessor when they are not.

Step 2 — Introduce a dummy activity to separate the two completions. Create a new event, event 2, representing specifically 'P is complete.' Draw activity P from event 1 to event 2 (duration 3 days). Draw activity Q directly from event 1 to event 4 (duration 5 days) — Q no longer shares both endpoints with P. Draw a dummy activity (dashed arrow, zero duration) from event 2 to event 4, purely to preserve the logical fact that reaching event 4 requires event 2 (P) to have already happened, without itself representing any real task.

Step 3 — Attach activity R correctly. Since R depends only on P, not on Q, draw R starting from event 2 (the 'P is complete' event) — not from event 4. This correctly shows that R can begin as soon as P finishes, regardless of whether Q (which may take longer, at 5 days) has finished or not. …

Simply drawing P and Q as two separate arrows both directly connecting event 1 to event 4 (without a dummy) is the exact violation this question is built around — it may look harmless when only durations are being added up, but it silently dest …