Identity Relation on Set \( A = \{a, b, c\} \)
📺 Video Explanation
📝 Question
Write the identity relation on the set:
\[ A = \{a, b, c\} \]
✅ Solution
🔹 Definition
The identity relation on a set \( A \) is:
\[ R = \{(x,x) : x \in A\} \]
That is, every element is related only to itself.
🔹 Apply to Given Set
For \( A = \{a, b, c\} \):
\[ (a,a),\ (b,b),\ (c,c) \]
So, the identity relation is:
\[ R = \{(a,a), (b,b), (c,c)\} \]
🎯 Final Answer
\[ \boxed{R = \{(a,a), (b,b), (c,c)\}} \]
🚀 Exam Insight
- Identity relation always has pairs of form (x,x)
- Number of elements = size of set
- Always reflexive, symmetric, and transitive