Let R be the relation on the set Z defined by xRy iff x − y is an integer. Prove that R is anequivalence relation on Z.
Question
Let R be the relation on the set Z defined by xRy iff x − y is an integer. Prove that R is anequivalence relation on Z.
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Solution 1
To prove that ( R ) is an equivalence relation on ( \mathbb{Z} ), we need to show that ( R ) is reflexive, symmetric, and transitive.
- Reflexive: A relation ( R ) on a set ( A ) is reflexive if every element is related to itself. That is, for all ( x \in \mathbb{Z} ), ( xRx ) mu Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob
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