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Unformatted text preview: 8 possibilities. So there are eight such relations. If the relation is also antisymmetric, then none of (1 ; 2) , (1 ; 3) , or (2 ; 3) can be in it, so there is only one such relation: the equality relation. 4. For the equivalence relation R = f (1 ; 1) ; (2 ; 2) ; (2 ; 3) ; (3 ; 2) ; (3 ; 3) g on f 1 ; 2 ; 3 g , nd the equivalence classes [1] and [3] . The equivalence class [1] is the set of elements of f 1 ; 2 ; 3 g that are related to 1 . So [1] = f 1 g . Similarly, [3] = f 2 ; 3 g ....
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 Spring '08
 STAFF

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