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It looks like you've uploaded an image from a math textbook. The image shows exercises involving relations between sets. Here's a breakdown of the tasks in the image:

1. **Task 1:**  
   "Write \( R \) and represent it by an arrow diagram."  
   This is asking you to define the relation \( R \) and then represent it graphically, likely by showing how elements of one set map to elements of another set.

2. **Task 2:**  
   "If \( 2 \,a\, R \,3 \), find the value of \( a \)."  
   This seems to refer to a specific relation \( R \) that connects elements of two sets, and you're tasked with determining the value of \( a \) when given \( 2 R 3 \).

3. **Task 3:**  
   "If \( X = \{2, 3, 4\} \), \( Y = \{6, 9, 12, 15\} \) and \( R \) is a relation from \( X \) to \( Y \) where 'a R b' means '3a = b' for each \( a \in X \) and \( b \in Y \), write \( R \) and represent it by an arrow diagram. Also, show that \( R \) is a function from \( X \) to \( Y \)."  
   This problem asks you to write the relation \( R \), show the connections between elements of \( X \) and \( Y \) (using the rule \( 3a = b \)), and prove that this relation is a function (which likely means each element of \( X \) is associated with exactly one element in \( Y \)).

Would you like assistance solving any of these exercises or further explanations on how to represent relations? Let me know which one you'd like to focus on!

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Here are 5 questions that can expand on this information:
1. What is the general definition of a relation between two sets?
2. How can we determine if a relation is a function?
3. How do we represent a relation using an arrow diagram?
4. What does it mean for a relation to satisfy a certain rule (e.g., \( 3a = b \))?
5. How would we verify that a relation is injective or surjective?

**Tip:** When working with relations, always check if every element in the domain has a unique image in the range to confirm it's a function!

The original question submitted by the user as text.

Explore how to represent relations and functions between sets using arrow diagrams. Solve problems involving the relation R where 3a = b, and show that the relation is a function. Suitable for high school students in Grades 10-12.

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