09-07-homework-1 - 2 or each of the following four...

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Sets and Logic — Fall 2011 due Wednesday, 9/15/11 Homework #1 1 This problem has three parts. a. Analyze the logical form of the statement If it is raining, then it is windy and the sun is not shining. b. Analyze the logical form of the statement Rain is a suFcient condition for wind with no sunshine. Is this statement equivalent to the statement in part a? c. Analyze the logical form of the statement Rain is a necessary condition for wind with no sunshine. Is this statement equivalent to the statement in part a?
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Unformatted text preview: 2 or each of the following four propositions, determine if they are true or false for all natural numbers. a. x y (2 x-y = 0). b. x ( x < 10- y ( y < x- y < 9)). c. y z ( y + z = 100). d. x y ( y > x z ( y + z = 100)). 3 Show that the statements A B and A \ B = are equivalent by writing each in logical symbols and then showing that the resulting formulas are logically equivalent....
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This note was uploaded on 12/10/2011 for the course MHF 3202 taught by Professor Larson during the Fall '09 term at University of Florida.

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