COMEDK · Maths · 20. Sets and Relations
In the set \(\mathrm{W}\) of whole numbers an equivalence relation \(\mathrm{R}\) is defined as follows \(\mathrm{aRb}\) iff both \(\mathrm{a}\) & \(\mathrm{~b}\) leave the same reminder when divided by 5. The equivalence class of 1 is given by.
- A \(\{4,9,14,19------\}\)
- B \(\{0,5,10,15------\}\)
- C \(\{2,7,12,17------\}\)
- D \(\{1,6,11,16------\}\)
Answer & Solution
Correct Answer
(D) \(\{1,6,11,16------\}\)
Step-by-step Solution
Detailed explanation
The relation \(R\) is defined on the set of whole numbers \(W = \{0, 1, 2, 3, \dots\}\) such that \(aRb\) if and only if \(a \equiv b \pmod{5}\). The equivalence class of an element \(x\), denoted by \([x]\), is the set of all elements \(y \in W\) such that \(yRx\). For…
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