Question

Define a relation R from the set of real numbers to itself as follows: Let x and y be real numbers. Then (x, y) ∈ R if x = y or x - y is an irrational number. Prove or disprove that R is an equivalence relation.

Name: define a relation r from the set of real numbers to itself as follows let x and y be real numbers then x y i r if x y or x y is an irrational number prove or disprove that r is an equivalenc 24495
Uploaded: 2023-04-06T13:38:26-08:00
Duration: 4 min 34 s
Channel: Madhur L
Description: define a relation r from the set of real numbers to itself as follows let x and y be real numbers then x y i r if x y or x y is an irrational number prove or disprove that r is an equivalenc 24495

          Define a relation R from the set of real numbers to itself as
follows: Let x and y be real numbers. Then (x, y) ∈ R if x = y or x
- y is an irrational number. Prove or disprove that R is an
equivalence relation.

Added by Carla R.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

04/06/2023

Step 1

Reflexive: For a relation to be reflexive, (x, x) must be in R for all x in the set of real numbers. Since x - x = 0, which is not irrational, we have x = x, so (x, x) is in R. Therefore, R is reflexive. Show more…

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Define a relation R from the set of real numbers to itself as follows: Let x and y be real numbers. Then (x, y) ∈ R if x = y or x - y is an irrational number. Prove or disprove that R is an equivalence relation.