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A set of mathematical problems from an examination held in spring 1995. The problems cover various topics including logic, sets, and number theory. Students are required to use concepts such as power sets, boolean algebra, and the euclidean algorithm to solve the problems.
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T F The contrapositive of the statement I finished my work implies I could go to a movie is the statement I did not go to a movie implies I did not finish my work.
T F The set of positive integers and the set of negative integers partition the set of the integers.
T F If a,b,q, and r are integers with 0 < r < b and a = bq + r, then gcd(a,b) = gcd(b,r).
Theorem 4: If a,b,q, and r are positive integers with a = bq + r and 0< r < b, then gcd(a,b) = gcd(b,r).