## Related questions with answers

Question

Consider the equivalence relation R={(x,y)|c-y is an integer}. a) What is the equivalence class of 1 for this equivalence relation? b) What is the equivalence class of 1/2 for this equivalence relation?

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 3a) $R = \{ (x, y) : x-y \in \mathbb{Z}\} \Rightarrow [1]_R = \{ y : (1, y) \in R\} = \{ y : 1-y \in \mathbb{Z}\} = \mathbb{Z}$.

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