My Math Forum Equivalence relations

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 June 12th, 2010, 11:08 PM #1 Member   Joined: Feb 2009 Posts: 76 Thanks: 0 Equivalence relations I honestly don't understand what my prof is trying to ask me. He writes his own problems and I can barely read his handwriting. "let $\ S= { (a,b) | a,b \varepsilon \mathbb{Z}, b \neq 0}\$ (a,b) is equivalent to (c,d) if ad = bc. (we write this as (a,b) ~ (c,d) Show that ~ is an equivalent relation. " I know that an equivalence relation is a reflexive (a,a) E R , symmetric (a,b) E R then (b,a) E R and transitive (a,b) E R and (b, c) E R then (a,c) E R. But I don't know where to begin
June 13th, 2010, 12:10 AM   #2
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Re: Equivalence relations

Quote:
 Originally Posted by remeday86 I honestly don't understand what my prof is trying to ask me. He writes his own problems and I can barely read his handwriting. "let $\ S= { (a,b) | a,b \varepsilon \mathbb{Z}, b \neq 0}\$ (a,b) is equivalent to (c,d) if ad = bc. (we write this as (a,b) ~ (c,d) Show that ~ is an equivalent relation. " I know that an equivalence relation is a reflexive (a,a) E R , symmetric (a,b) E R then (b,a) E R and transitive (a,b) E R and (b, c) E R then (a,c) E R. But I don't know where to begin
(a, b) ~ (c, d) means ad = bc, so ~ is reflexive ("(a, b) ~ (a, b) for all (a, b)") is ab = ba for all (a, b). This is true since integer multiplication is commutative. Translate the statements of transitive and symmetric in the same way.

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