 My Math Forum On the set N × N, define the following relation: (a, b) ∼ (c, d) if and only if a + d

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 October 16th, 2019, 12:16 PM #1 Newbie   Joined: Sep 2019 From: Toronto Posts: 7 Thanks: 0 On the set N × N, define the following relation: (a, b) ∼ (c, d) if and only if a + d On the set N × N, define the following relation: (a, b) ∼ (c, d) if and only if a + d = b + c. (1) Show that this is an equivalence relation (2) Describe the equivalence class of (1, 1) October 16th, 2019, 01:04 PM   #2
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Quote:
 Originally Posted by enimasj On the set N × N, define the following relation: (a, b) ∼ (c, d) if and only if a + d = b + c. (1) Show that this is an equivalence relation (2) Describe the equivalence class of (1, 1)
Well, to start with, let x = (a1, b1), y = (a2, b2), and z = (a3, b3). Then an equivalence relation is reflexive (x ~ x), symmetric (x ~ y) implies (y ~ x), and transitive (x ~ y) and (y ~ z) implies (x ~ z). Which, if any of them, is true?

-Dan

Last edited by topsquark; October 16th, 2019 at 01:08 PM. Tags ∼, define, proofs, relation, set Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post sMilips Abstract Algebra 1 December 2nd, 2018 09:04 PM Ganesh Ujwal Real Analysis 0 January 5th, 2015 12:37 AM uniquegel Algebra 4 September 8th, 2014 05:18 PM Zhai Applied Math 1 May 10th, 2012 10:25 PM Qer Algebra 1 March 4th, 2010 01:53 PM

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