JEE Mains · Maths · STD 12 - 1. relation and function
Let \(A=\{2,3,6,8,9,11\}\) and \(B=\{1,4,5,10,15\}\) Let \(\mathrm{R}\) be a relation on \(\mathrm{A} \times \mathrm{B}\) define by \((\mathrm{a}, \mathrm{b}) \mathrm{R}(\mathrm{c}, \mathrm{d})\) if and only if \(3 \mathrm{ad}-7 \mathrm{bc}\) is an even integer. Then the relation \(\mathrm{R}\) is
- A reflexive but not symmetric.
- B transitive but not symmetric.
- C reflexive and symmetric but not transitive.
- D an equivalence relation.
Answer & Solution
Correct Answer
(C) reflexive and symmetric but not transitive.
Step-by-step Solution
Detailed explanation
\( \mathrm{A}=\{2,3,6,8,9,11\} \quad(\mathrm{a}, \mathrm{b}) \mathrm{R}(\mathrm{c}, \mathrm{d}) \) \( \mathrm{B}=\{1,4,5,10,15\} \quad 3 \mathrm{ad}-7 \mathrm{bc} \) \( \text { Reflexive : }(\mathrm{a}, \mathrm{b}) \mathrm{R}(\mathrm{a}, \mathrm{b})\)…
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