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Unformatted text preview: a Boolean circuit, using only AND, OR and NOT gates, that implements the function P ARITY as efﬁcient as possible. (Efﬁcient here means: with as few a number of gates as possible.) You do not have to draw the full circuit; it is sufﬁcient to describe how you would draw it if you would have to. Question 5 (Formulas with quantiﬁers, 3 points) . Let f be a continuous function from the real numbers R to the real numbers R and consider the statement ∀ x ∃ y [ f ( x ) > y ] implies ∃ y ∀ x [ f ( x ) > y ] . Give an example of a function f that disproves this alleged implication. Explain brieﬂy your line of reasoning behind your construction....
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This note was uploaded on 12/27/2011 for the course CMPSC 40 taught by Professor Egiceoclu during the Fall '09 term at UCSB.
 Fall '09
 Egiceoclu

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