Question:
The relation \( R = \{(1,3), (2,3), (2,4), (3,1), (4,4), (4,1)\} \) on the set \( X = \{1,2,3,4\} \) is:
The relation \( R = \{(1,3), (2,3), (2,4), (3,1), (4,4), (4,1)\} \) on the set \( X = \{1,2,3,4\} \) is:
Show Hint
Check for pairs $(a, b)$ where $(b, a)$ is missing to quickly disprove symmetry.
Updated On: Apr 28, 2026
- a 1-1 function
- reflexive
- transitive
- not symmetric
- an onto function
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Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Concept
A relation is symmetric if $(a, b) \in R$ implies $(b, a) \in R$.
Step 2: Analysis
In the given relation $R$, we have $(2, 3) \in R$. For the relation to be symmetric, $(3, 2)$ must also be in $R$.
Step 3: Conclusion
Since $(3, 2) \notin R$, the relation is not symmetric. Final Answer: (D)
A relation is symmetric if $(a, b) \in R$ implies $(b, a) \in R$.
Step 2: Analysis
In the given relation $R$, we have $(2, 3) \in R$. For the relation to be symmetric, $(3, 2)$ must also be in $R$.
Step 3: Conclusion
Since $(3, 2) \notin R$, the relation is not symmetric. Final Answer: (D)
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