Question

Texts: Consider N = {1, 2, . . .}. Define a relation ∼ on N^2 via (i, j) ∼ (k, l) if i + l = j + k. (1) Show carefully that ∼ is an equivalence relation on N^2. That is, explain why the three defining properties of an equivalence relation are satisfied. (2) Enumerate five elements in [(1, 2)]. (3) Enumerate five elements in [(1, 1)]. How do you solve this?

Name: texts consider n 1 2 define a relation on n2 via i j k l if i l j k 1 show carefully that is an equivalence relation on n2 that is explain why the three defining properties of an equivalence 43786
Uploaded: 2022-08-27T01:46:46-08:00
Duration: 3 min 52 s
Channel: Vincenzo Zaccaro
Description: texts consider n 1 2 define a relation on n2 via i j k l if i l j k 1 show carefully that is an equivalence relation on n2 that is explain why the three defining properties of an equivalence 43786

          Texts: Consider N = {1, 2, . . .}. Define a relation ∼ on N^2 via (i, j) ∼ (k, l) if i + l = j + k. 

(1) Show carefully that ∼ is an equivalence relation on N^2. That is, explain why the three defining properties of an equivalence relation are satisfied. 

(2) Enumerate five elements in [(1, 2)]. 

(3) Enumerate five elements in [(1, 1)]. 

How do you solve this?

Added by Michelle W.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Vincenzo Zaccaro

08/27/2022

Step 1

Since i + j = i + j, we can see that (i, j) ∼ (i, j) holds. Show more…

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Texts: Consider N = {1, 2, . . .}. Define a relation ∼ on N^2 via (i, j) ∼ (k, l) if i + l = j + k. (1) Show carefully that ∼ is an equivalence relation on N^2. That is, explain why the three defining properties of an equivalence relation are satisfied. (2) Enumerate five elements in [(1, 2)]. (3) Enumerate five elements in [(1, 1)]. How do you solve this?