Exercise · ZW-EQUIVALENCE-CLASS-008 · ★★☆ Intermediate
Let \(A=\{1,2,3,4\}\) and \(R\) an equivalence relation with classes \(\{1,2\}\) and \(\{3,4\}\). What is \([2]\)?
Choose one option.
Show answer
- C. \(\{1,2\}\)
Explanation
\([2]\) is the class containing \(2\), which here is \(\{1,2\}\), since \(1\) and \(2\) are related. The class of \(2\) is not a singleton.
Review the concept: Equivalence class
Given an equivalence relation \(R\) on \(A\) and an element \(a\in A\), the equivalence class \([a]\) is the set of all \(x\in A\) with \(x\,R\,a\).
\[[a]=\{x\in A : x\,R\,a\}\]
More practice problems: equivalence class
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