Question

2. Define a relation \(R\) on \(\mathbb{R}\) by: \(a \sim b \iff b - a \in \mathbb{Z}\). (a) Prove that this is an equivalence relation. (b) Describe the collection of all distinct equivalence classes of \(R\).

          2. Define a relation \(R\) on \(\mathbb{R}\) by: \(a \sim b \iff b - a \in \mathbb{Z}\).
(a) Prove that this is an equivalence relation.
(b) Describe the collection of all distinct equivalence classes of \(R\).

2. Define a relation R on ℝ by: a ∼ b b - a ∈ℤ.
(a) Prove that this is an equivalence relation.
(b) Describe the collection of all distinct equivalence classes of R.

Added by Jordan J.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

07/26/2023

Step 1

Since a - a = 0, which is an integer, the reflexive property holds. Show more…

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Define a relation R on R by: a ~ b ⇒ b - a ∈ Z. (a) Prove that this is an equivalence relation. (b) Describe the collection of all distinct equivalence classes of R. 2. Define a relation R on R by a ~ b ⇒ b - a ∈ Z. (a) Prove that this is an equivalence relation. (b) Describe the collection of all distinct equivalence classes of R.