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hw1_1

# hw1_1 - CS153 Autumn 2009 Homework 1 Due Tuesday October...

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CS153 Autumn 2009: Homework 1 Due Tuesday, October 13th at 3PM 1. (10 points) Prove that proof by contrapositive is valid. In other words, show that the statements “if A then B ” ( A B) and “if not B then not A ” ( ¬ B → ¬ A ) are equivalent by using a truth table. 2. (6 points) Prove the following statement about integers: if a 2 is even, then a is even. 3. (10 points) Based on Hein, Page 34, Exercise 24 In lecture, we started the proof that “power( A B ) = power( A ) power( B )” by showing that “power( A B ) power( A ) power( B )”. Complete the proof by showing that “power( A ) power( B ) power( A B )”. 4. (6 points) Write down the converse of the following statement about integers: “If x and y sum to 10, then they must have the same parity.” 5. (8 points) Hein page 32, Exercise 10, Parts b, d, f, and h. For each integer i define A i as follows: If i is even then A i = { x | x Z and x < - i or i < x } . If i is odd then A i = { x | x Z and - i < x < i } .

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