7. For each of the directed graphs below, determine the minimum number of arrows you would need to add

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Transcription for Educational Use:**

**Problem 7:**

For each of the directed graphs below, determine the *minimum* number of arrows you would need to add to the directed graph in order for it to be an equivalence relation (a double-headed arrow counts as two). You do not need to justify your answers for this problem.

**a)**

- Diagram: Three nodes in a triangular configuration.
- Arrows: One arrow points from the top node to the bottom right node, and another arrow points from the bottom left node to the top node.

**Minimum: __________**

---

**b)**

- Diagram: Three nodes forming a triangle.
- Arrows: There is an arrow pointing from the bottom left node to the top node, an arrow from the top node to the bottom right node, and an arrow from the bottom right node to the bottom left node.

**Minimum: __________**

---

**c)**

- Diagram: Two nodes.
- Arrows: There is a double-headed arrow between the two nodes.

**Minimum: __________**
Transcribed Image Text:**Transcription for Educational Use:** **Problem 7:** For each of the directed graphs below, determine the *minimum* number of arrows you would need to add to the directed graph in order for it to be an equivalence relation (a double-headed arrow counts as two). You do not need to justify your answers for this problem. **a)** - Diagram: Three nodes in a triangular configuration. - Arrows: One arrow points from the top node to the bottom right node, and another arrow points from the bottom left node to the top node. **Minimum: __________** --- **b)** - Diagram: Three nodes forming a triangle. - Arrows: There is an arrow pointing from the bottom left node to the top node, an arrow from the top node to the bottom right node, and an arrow from the bottom right node to the bottom left node. **Minimum: __________** --- **c)** - Diagram: Two nodes. - Arrows: There is a double-headed arrow between the two nodes. **Minimum: __________**
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