JEE Mains · Maths · STD 12 - 1. relation and function
Let \(R\) be a relation on \(Z \times Z\) defined by\( (a, b)\)\(R(c, d)\) if and only if \(ad - bc\) is divisible by \(5\) . Then \(\mathrm{R}\) is
- A Reflexive and symmetric but not transitive
- B Reflexive but neither symmetric not transitive
- C Reflexive, symmetric and transitive.
- D Reflexive and transitive but not symmetric
Answer & Solution
Correct Answer
(A) Reflexive and symmetric but not transitive
Step-by-step Solution
Detailed explanation
\((a, b) R(a, b)\) as \(a b-a b=0\) Therefore reflexive Let \((a, b) R(c, d) \Rightarrow a d-b c\) is divisible by \(5\) \(\Rightarrow \mathrm{bc}-\mathrm{ad}\) is divisible by \(5 \Rightarrow(\mathrm{c}, \mathrm{d}) \mathrm{R}(\mathrm{a}, \mathrm{b})\) Therefore symmetric…
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