JEE Mains · Maths · STD 12 - 1. relation and function
Let A be the set of all functions \(f: \mathbf{Z} \rightarrow \mathbf{Z}\) and R be a relation on A such that \(\mathrm{R}=\{(\mathrm{f}, \mathrm{g}): f(0)=\mathrm{g}(1)\) and \(f(1)=\mathrm{g}(0)\}\). Then R is:
- A Symmetric and transitive but not reflective
- B Symmetric but neither reflective nor transitive
- C Reflexive but neither symmetric nor transitive
- D Transitive but neither reflexive nor symmetric
Answer & Solution
Correct Answer
(B) Symmetric but neither reflective nor transitive
Step-by-step Solution
Detailed explanation
\begin{aligned} & \mathrm{R}=\{(\mathrm{f}, \mathrm{g}): \mathrm{f}(0)=\mathrm{g}(1) \text { and } \mathrm{f}(1)=\mathrm{g}(0)\} \\ & \text { Reflexive: }(\mathrm{f}, \mathrm{f}) \in \mathrm{R} \\ & =\mathrm{f}(0)=\mathrm{f}(1) \text { and } \mathrm{f}(1)=\mathrm{f}(0)…
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