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Unformatted text preview: for content and correctness. Name 4. [4 pt each] TRUE or FALSE (spell out the word) (a) A for any set A . (b) If A and B are nite sets, then  A B  =  A   B  (c) If R is an equivalence relation on a set A , then R cannot be antisymmetric. (d) x Z , y Z , ( x + y )  (e) For every x N , n Y k =1 (2 k ) = 2 n n ! 5. [15 pt] Prove or disprove: If A,B and C are sets such that A B C , then A B C . Name 6. [15 pt] Use a truth table proof to prove that x ( x y ) is logically equivalent to x y . 7. [7 pt] Let R be a symmetric relation on on a nite set A that is irreexive. Briey explain why R must have an even number of elements. Hint: if A is not empty, then R has no ordered pairs of the form ( x,x ). The only other kind of ordered pair allowed in R will then be of the form ( x,y ). But, R is symmetric!...
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This note was uploaded on 03/19/2010 for the course EOE 342 taught by Professor Jooe during the Spring '10 term at Albany College of Pharmacy and Health Sciences.
 Spring '10
 Jooe

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