quiz3_key - COT 3100 Summer 2001 Quiz #3 (Solutions)...

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COT 3100 Summer 2001 Quiz #3 (Solutions) 06/21/2001 1. If {{ a , c , e }, { b , d , f }} is a partition of the set A = { a , b , c , d , e , f }, determine the corresponding equivalence relation R . For the relation that corresponds to the given partition, we have A / R ={{ a , c , e }, { b , d , f }}, so there are two equivalence classes: [ a ] R = { a , c , e }, and [ b ] R = { b , d , f }. Using the definition of equivalence classes and properties of equivalence relations we can find: R = {( a , a ), ( b , b ), ( c , c ), ( d , d ), ( e , e ), ( f , f ), ( a , c ), ( a , e ), ( c , e ), ( c , a ), ( e , a ), ( e , c ), ( b , d ), ( b , f ), ( d , f ), ( d , b ), ( f , b ), ( f , d )} 2. Consider the following relation R on the set A = {1, 2, 3, 4}: R = {(1, 2), (2, 3), (3, 1), (4, 1)} Find the transitive closure of this relation. We can find all pairs of elements in
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