Relation “y is One Half of x” on Set \( A \)

📺 Video Explanation

📝 Question

Let:

\[ A = \{1,2,3,4,5,6,7,8\} \]

Relation \( R \) is defined as:

\[ R = \{(x,y) : y \text{ is one half of } x,\ x,y \in A\} \]

Write \( R \) as a set of ordered pairs.

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✅ Solution

🔹 Step 1: Write Condition

“y is one half of x” means:

\[ y = \frac{x}{2} \]

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🔹 Step 2: Check Values of x

We need \( y \in A \), so \( x \) must be even.

• \( x = 2 \Rightarrow y = 1 \)
• \( x = 4 \Rightarrow y = 2 \)
• \( x = 6 \Rightarrow y = 3 \)
• \( x = 8 \Rightarrow y = 4 \)

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🔹 Step 3: Write Ordered Pairs

\[ (2,1), (4,2), (6,3), (8,4) \]

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🎯 Final Answer

\[ \boxed{R = \{(2,1), (4,2), (6,3), (8,4)\}} \]

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🚀 Exam Insight

• Convert statement into equation first
• Only even numbers work here
• Always ensure both x and y belong to the set