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Question: question 21 p1 prove that the sum of two even...

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Question 2.1 (P1) Prove that the sum of two even numbers, ni and n2, is also even. Question 2.2 (PI) Prove that the sum of two odd numbers, j and k, is even. Question 2.3 (C1) At Dallas Fort Worth International Airport, there 1,850 flights per day (as found at http://dfwairport.mediaroom.com/DFWInfoSheet). Using the Pigeonhole Principle, prove that there is a 2- minute window in which at least 3 flights take off. (It may help to first state: What are the pigeons which wil match, and what are pigeonholes?) Question 2.4 (P1) The following if-then statements are true. Prove them. a) (About a polygon P): If P is a square, then P is a rectangle. b) (About an integer m): If m is a multiple of 6, then m is a multiple of 3. c) If you own a dog, then you are a pet-owner. d) (About a playing card, c): If cs suit is diamonds, then cs suit is red. Question 2.5 (P1) The following if-then statements are false. Prove they are false by finding explicit counterexamples a) (About a polygon R): If R is a rectangle, then R is a square. b) (About an integer n): If n is a multiple of 3, then n is a multiple of 6. c) If you are a pet-owner, then you have a dog. d) (About a playing card ): If ds suit is red, then ds suit is diamonds. e) If a person lives in Texas, then they live in Houston.
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