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Unformatted text preview: ) R ( p,q ) if and only if mq = np . (a) (8 pts.) Prove that R is an equivalence relation. (b) (3 pts.) List 3 elements of (3 , 4) /R . 5. Dene the relation R on N N by ( m,n ) S ( p,q ) if and only if m p and n q . (a) (8 pts.) Prove that S is antisymmetric on N N . (In fact, it is a partial order.) (b) (3 pts.) Is S a linear order ? Why or why not? 6. (8 pts.) For each a R , let A a = { ( x,y ) R R : x + y = a } . Prove that for each a, b R , A a A b = or A a = A b ....
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 Fall '08
 Alligood,K
 Math, Advanced Math

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