Math245FinalSum00

Math245FinalSum00 - Math 245 Name FINAL The final will be...

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Math 245 Name: ________________________ FINAL The final will be scored out of 175 points (175 points = 100%), and then your score will be renormalized so that the total possible on the final is 300 points. Show all work where appropriate! 1) Let p and q be propositions. Write the truth table for the proposition ¬ p q ( ) [ ] q . (15 points) 2) Let the universe of discourse for x , y , and z be the set of all rational numbers. For each of the propositions below, indicate whether it is True (T) or False (F). (10 points total; 5 points each) a) x y x y = 1 __________ b) x y z xy = z ( ) __________
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3) Let A and B be sets. Completely simplify A B B ( ) A . (15 points) 4) Completely evaluate the sum 3 i i = 1 500 . Do not use "brute force". (15 points) 5) Let the function f : R R be defined by f x ( ) = 2 x . (10 points; 5 points each) a) Yes or No: Is f one-to-one? __________ b) Yes or No: Is f onto? __________
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6) A "perfect square" is any integer that is the square of an integer. How
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Math245FinalSum00 - Math 245 Name FINAL The final will be...

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