COMEDK · Maths · 20. Sets and Relations
Which of the following relations on the set of real numbers \(\mathrm{R}\) is an equivalence relation?
- A \(a R_4 b \Leftrightarrow a < b\)
- B \(a R_2 b \Leftrightarrow a \geq b\)
- C \(a R_1 b \Leftrightarrow|a|=|b|\)
- D \(a R_3 b \Leftrightarrow \text { adivides } b\)
Answer & Solution
Correct Answer
(C) \(a R_1 b \Leftrightarrow|a|=|b|\)
Step-by-step Solution
Detailed explanation
A relation \(R\) is an equivalence relation if it is reflexive, symmetric, and transitive. For option (1), \(a R_4 b \Leftrightarrow a < b\). This is not reflexive because \(a < a\) is false. It is not symmetric because \(a < b\) does not imply \(b < a\). For option (2),…
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