Week 5 Tutorial - consecutive locations that have a sum...

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Concordia University COMP 232/2 Mathematics for Computer Science FALL 2010 Tutorial Problems (Section DD) : Week 5 5-1. Find predicates P and Q such that ± x P ( x ) ² ± x Q ( x ) ² 6≡ ∀ x y ± P ( x ) Q ( y ) ² . 5-2. a) Prove that at least one of the real numbers a 1 , a 2 , . . . , a n is greater than or equal to the average of these numbers. What kind of proof did you use? b) Use part (a) above to show that if the first ten positive integers are placed around a circle, in any order, then there exist three integers in
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Unformatted text preview: consecutive locations that have a sum greater than or equal to 17. 5-3. a) Prove or disprove: If a and b are rational numbers, then a b is also rational. b) Construct a direct proof for the following: If 6 x + 9 y = 101 then x and y are not both integers. c) A perfect number is one which is the sum of all its divisors except itself. For example, 6 is perfect since 1 + 2 + 3 = 6. So is 28. Construct an indirect proof for the following: A perfect number is not a prime. 2-Oct-2010, 12:59 pm...
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