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Unformatted text preview: R is an equivalence relation and write down its equivalence classes. 5. Let S be the set f 1 ; 2 ; 3 ; 4 g and let X be the set S S . Dene a relation R on X by the rule ( a; b ) R ( c; d ) if and only if a + b = c + d . Show that R is an equivalence relation and list the equivalence classes. 6. Recall that if f : X ! Y is a function, then an equivalence relation R f is dened on X by the rule x 1 R f x 2 if and only if f ( x 1 ) = f ( x 2 ). For the function f : R 2 ! R by f ( a; b ) = a + b , determine the equivalence classes of each of the following elements of R 2 : (a) (1 ; 1), (b) (1 ; 1), (c) ( 2 ; 3). Math 4023 1...
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 Fall '09

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