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June 12th, 2010, 11:08 PM   #1
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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

(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
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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

(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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