define a relation r on z requiring that arb a b z if 2a b prove that r is an equivalence relatio

Name: define a relation r on z requiring that arb a b z if 2a b prove that r is an equivalence relation and identify all its equivalence classes 37363
Uploaded: 2023-08-08T10:24:50-08:00
Duration: 1 min 45 s
Channel: Sam Stansfield
Description: define a relation r on z requiring that arb a b z if 2a b prove that r is an equivalence relation and identify all its equivalence classes 37363

Question

Maitreya E · Accepted Answer

1. Reflexivity: We need to show that aRa for all a ∈ Z. Since a + a = 2a, and 2|(2a), we have aR

Question

Define a relation R on Z requiring that aRb, a, b ∈ Z, if 2|(a + b). Prove that R is an equivalence relation and identify all its equivalence classes.

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