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October 16th, 2019, 12:16 PM   #1
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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)
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October 16th, 2019, 01:04 PM   #2
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Originally Posted by enimasj View Post
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.
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