Exam 1 - For every real number x there is a natural number...

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MATH 290 – 25 FEBRUARY 2010 – EXAM 1 Answer all of the following questions on the answer sheets provided. Show all work, as partial credit may be given. This exam will be counted out of a total of 50 points. 1. (5 pts. each) Answer each of the following questions using a truth table. (a) Is [ P ( P = Q )] = Q a tautology? Justify your answer with a truth table or portion of a truth table. (b) Is P = Q logically equivalent to Q = P ? Justify your answer with a truth table or a portion of a truth table. (c) Give a useful denial in propositional form of P = Q . (d) Give a useful denial in English of the statement
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Unformatted text preview: For every real number x there is a natural number n such that x < n . 2. (8 pts.) Prove that for all natural numbers a , b , and c , if a divides b and a divides c then a divides b + c . 3. (8 pts.) Prove by contrapositive that for all natural numbers n , if n 2 is even then n is even. 4. (8 pts.) Prove by contradiction that for all natural numbers n , n n + 1 > n n + 2 . 5. (8 pts.) Prove that for any sets A , B , and C , if A B C and A B = then A C ....
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