Set, Relations and FunctionsMTP Dec 22 Series IIQuestion 1953 of 217
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Let A={1,2,3}\displaystyle A = \{1,2,3\} then the relation R={(1,1),(2,3),(2,2),(3,3),(1,2)}\displaystyle R = \{(1,1), (2,3), (2,2), (3,3), (1,2)\} is called

Options

ASymmetric
BTransitive
CReflexive
DEquivalence
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Correct Answer

✅ Option c — Reflexive

All Options:

  • ASymmetric
  • BTransitive
  • CReflexive
  • DEquivalence

Detailed Solution & Explanation

We are given set A={1,2,3}\displaystyle A = \{1,2,3\} and relation R={(1,1),(2,3),(2,2),(3,3),(1,2)}\displaystyle R = \{(1,1), (2,3), (2,2), (3,3), (1,2)\}.
Let's analyze the properties of R\displaystyle R:
1. **Reflexive**: Since (1,1),(2,2),(3,3)∈R\displaystyle (1,1), (2,2), (3,3) \in R, the relation is reflexive. This corresponds to Option C.
2. **Symmetric**: For the relation to be symmetric, since (1,2)∈R\displaystyle (1, 2) \in R, we must have (2,1)∈R\displaystyle (2, 1) \in R. But (2,1)∉R\displaystyle (2, 1) \notin R. Thus, the relation is not symmetric.
3. **Transitive**: For the relation to be transitive, since (1,2)∈R\displaystyle (1, 2) \in R and (2,3)∈R\displaystyle (2, 3) \in R, we must have (1,3)∈R\displaystyle (1, 3) \in R. But (1,3)∉R\displaystyle (1, 3) \notin R. Thus, the relation is not transitive.
Since the relation is not symmetric and not transitive, it cannot be an equivalence relation.
Therefore, the relation is only reflexive.
*Note: The relation is reflexive, which corresponds to Option C. The textbook answer key incorrectly lists Option D (Equivalence) as the correct choice.*
Hence, **Option C** is the correct answer.

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