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Unformatted text preview: M IDTERM EXAM INATION Nathan Redford CSC 226-002 10/14/2008 19. If we align one set across the top of the diagram and the other down the left hand side of the diagram, we can list all cartesian products at the intersections of the sets. We can then count diagonally starting with (1 , 1) then (2 , 1), (1 , 2), (3 , 1), (2 , 2), (1 , 3), ... (n , m) and are able to put all the products into a one to one correspondence with the natural numbers which by definition makes the cartesian product of two countably infinite sets countably infinite. 20. Given a|b Given a|c (Let x and y equal integers) Because a divides b and c: xa = b ya = c (Let s and t equal integers) sb = asx tc = aty sb + tc = asx + aty sb + tc = a(sx + ty) Because a is multiplied by (sx + ty) which is an integer: a|(sb + tc) ...
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This note was uploaded on 04/28/2009 for the course CSC 226 taught by Professor Watkins during the Spring '08 term at N.C. State.
- Spring '08