# Activity-on-Arrow (AOA) Diagram Below is the **AOA (Activity-on-Arrow)** diagram for the given activities and their immediate predecessors. In an AOA diagram, **nodes** represent events (start or completion of activities), and **arrows** represent activities. ## **Activity List** | Activity | Immediate Predecessor(s) | |----------|-------------------------| | A | — | | B | — | | C | A | | D | A | | E | B | | F | B | | G | C, E | | H | D, F | --- ## **Step-by-Step Construction** ### **1. Start Node** - Draw a **Start node (Node 1)**. ### **2. Activities with No Predecessors** - **A**: Arrow from Node 1 to Node 2 (A) - **B**: Arrow from Node 1 to Node 3 (B) ### **3. Activities with A as Predecessor** - **C**: Arrow from Node 2 to Node 4 (C) - **D**: Arrow from Node 2 to Node 5 (D) ### **4. Activities with B as Predecessor** - **E**: Arrow from Node 3 to Node 6 (E) - **F**: Arrow from Node 3 to Node 7 (F) ### **5. Activities with Multiple Predecessors** - **G** (C and E): Both C (Node 4) and E (Node 6) must finish before G can start. - Create a dummy activity from Node 4 to Node 8. - Arrow from Node 6 to Node 8 (G starts at Node 8). - **H** (D and F): Both D (Node 5) and F (Node 7) must finish before H can start. - Create a dummy activity from Node 5 to Node 9. - Arrow from Node 7 to Node 9 (H starts at Node 9). --- ## **AOA Diagram (Textual Representation)** ``` (1)---A--->(2)---C--->(4) | | | +---D--->(5) | +---B--->(3)---E--->(6) | | | +---F--->(7) | (C, E) G: Dummy from (4) to (8), E from (6) to (8), G from (8) onwards (D, F) H: Dummy from (5) to (9), F from (7) to (9), H from (9) onwards ``` --- ## **AOA Diagram (Visual Sketch)** Here is a basic sketch (you can draw this by hand or use diagramming tools): ```plaintext [Start] / \ A B / \ [2] [3] / \ / \ C D E F | | | | [4] [5] [6] [7] \ | \ | \ | \ | \ | \ | [8] [9] | | G H ``` - **Dummy arrows**: To represent activities with multiple predecessors, use dashed lines or label as "dummy" in your drawing. --- ### **Tips for Drawing:** - Use circles or boxes for **nodes/events**. - Use arrows for **activities**; label each arrow with its activity name. - Use dashed arrows for **dummy activities**. --- ## **Summary Table of Nodes** | Node | Description | |------|---------------------------| | 1 | Start | | 2 | After A | | 3 | After B | | 4 | After C | | 5 | After D | | 6 | After E | | 7 | After F | | 8 | Predecessors C & E join (for G) | | 9 | Predecessors D & F join (for H) | --- **If you want a ready-to-use diagram, let me know if you prefer a hand-drawn image or a diagramming tool output!**