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# plugin-hw1 - CS206 HW1 Sept 8 2009(Write up convincing...

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CS206 HW1 Sept. 8, 2009 (Write up convincing answers to the questions marked by an asterisk (*). Some of the unstarred questions will be worked in recitation. (**) indicates a more challenging problem, not required to hand in unless you want feedback - its not part of the grading. Your solutions are due in class on Wednesday, September 16, 2009.) 1. (Sets) Prove the following facts, in the manner indicated. (a) (deMorgan 1) ( S n i =1 A i ) c = T n i =1 ( A c i ). Do this by induction. (b) (*) (deMorgan 2) ( T n i =1 A i ) c = S n i =1 ( A c i ). Do this one both by induction , and without induction. 2. (Sets) Decide whether the following statements are TRUE or FALSE and give a convincing argument to support your claim; if FALSE, you should offer a counterexample. (a) (*) ( A B ) \ C = A ( B \ C ). (b) ( A B ) \ A = B . (c) (*) ( A \ B ) B = A (d) ( A B ) = ( A \ B ) ( B \ A ) ( A B ). (e) (*) ( A B ) c \ A c = B c (f) T n i =1 A i A 1 . (g) (*) A 1 S n i =1 A i . (h) S n i =1 A i S m + n i =1 A i , m > 0; (i.e., S k i =1 A i increases with k ).

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