Check Ordered Pairs in Relation
📺 Video Explanation
📝 Question
Let relation \( R \) on \( \mathbb{N} \) be defined as:
\[ (a,b) \in R \iff a = b – 2,\quad b > 6 \]
Check which of the following belongs to \( R \):
- (a) \( (2,4) \)
- (b) \( (3,8) \)
- (c) \( (6,8) \)
- (d) \( (8,7) \)
✅ Solution
🔹 Check Option (a): \( (2,4) \)
Condition: \[ a = b – 2 \Rightarrow 2 = 4 – 2 = 2 \]
True, but: \[ b = 4 \not> 6 \]
❌ Not in \( R \)
🔹 Check Option (b): \( (3,8) \)
\[ 3 = 8 – 2 = 6 \]
False.
❌ Not in \( R \)
🔹 Check Option (c): \( (6,8) \)
\[ 6 = 8 – 2 = 6 \]
True and: \[ 8 > 6 \]
✔ This pair belongs to \( R \)
🔹 Check Option (d): \( (8,7) \)
\[ 8 = 7 – 2 = 5 \]
False.
❌ Not in \( R \)
🎯 Final Answer
\[ \boxed{(6,8) \in R} \]
✔ Correct option: (c)
🚀 Exam Insight
- Check both equation and extra condition
- Don’t stop after satisfying only one condition
- MCQs often trap with partial truth