Relation “a is a Divisor of b” from A to B

📺 Video Explanation

📝 Question

Let:

\[ A = \{2,3,4,5\}, \quad B = \{1,3,4\} \]

Relation \( R \) is defined as:

\[ (a,b) \in R \iff a \text{ divides } b \]

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

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✅ Solution

🔹 Step 1: Check Divisibility

• For \( a = 2 \): 2 divides 4 ✔ → (2,4)
• For \( a = 3 \): 3 divides 3 ✔ → (3,3)
• For \( a = 4 \): 4 divides 4 ✔ → (4,4)
• For \( a = 5 \): 5 divides none → no pair

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🔹 Step 2: Write Relation

\[ R = \{(2,4), (3,3), (4,4)\} \]

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🎯 Final Answer

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

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🚀 Exam Insight

• “a divides b” ⇒ \( b \div a \) is integer
• Check each pair systematically
• Don’t forget self-division (like 3 divides 3)