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Unformatted text preview: MATH 74 HOMEWORK 4 (DUE WEDNESDAY SEPTEMBER 26) If you are going to prove a statement P by contradiction, you follow the basic for- mat “Assume P is false. Then [deductions, arriving at a contradiction]. Therefore P is true.” In order to use this technique effectively, you need to make deductions from a statement of the form “P is false.” If P is a complicated statement, this requires a certain amount of attention to detail. Very often, the first and fatal mistake of a proof of P by contradiction is an incorrect interpretation of what it means for P to be false. 1. Consider the statement “for any integers x , y , and z , we have x 3 + y 3 + z 3 6 = 33.” What would it mean if this statement is false? (a) For any integers x , y , and z , we have x 3 + y 3 + z 3 = 33 (b) If x 3 + y 3 + z 3 = 33, then x , y , and z are not integers. (c) There are integers x , y , and z for which x 3 + y 3 + z 3 = 33....
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This note was uploaded on 02/10/2010 for the course MATH 74 taught by Professor Courtney during the Fall '07 term at Berkeley.
- Fall '07