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GUJCET · Maths · Relations and Functions
\(R =\{(1,1),(2,2),(3,3)\}\) is defined on set\(\{x: x \in N, x < 4\}\) then relation \(R =\{(1,1),(2,2),(3,3)\}\) ____________ .
- A is reflexive and symmetric, but not transitive
- B is reflexive and transitive, but not symmetric
- C is symmetric and transitive, but not reflexive
- D is equivalence relation
Answer & Solution
Correct Answer
(D) is equivalence relation
Step-by-step Solution
Detailed explanation
Let \(A = \{x: x \in N, x < 4\} = \{1, 2, 3\}\). Reflexive: For all \(a \in A\), \((a,a) \in R\). \((1,1),(2,2),(3,3) \in R\). Hence, R is reflexive.
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