MATH 135 Midterm Solutions
1. (a) Write down the converse of If x is a perfect square, then x 0.
(b) Write down the contrapositive of If b > 8, then f (b) < 0 or f (b) = 99. (c) Determine (with brief justication) the second smallest positive i
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Algebra for Honours Mathematics
Instructor: B. Tasic
1. Show your work in the space provided. Be precise, concise and complete. If you need more space,
use the back of
Monday 15 October 2007, 7:00 p.m. to 8:15 p.m.
1. Let a, b, c Z. Suppose that P is the statement: If a | b or a | c, then a | bc.
(a) Write down the converse of P .
(b) Disprove the converse of P .
(c) Write down
1. Let A be the statement If n is an odd integer, then n2 + n is an even integer.
(a) (2 marks) Is A TRUE or FALSE? Justify your answer.
(b) (3 marks) State the converse of A. Is the converse of A TRUE or FALSE? Justify
(c) State the contrapo
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Math 135 - Fall 2001 Final Page I of I REPRINTED BY MATHSOC cfw_>4
Instructors: M. Bauer, L. Cummings, S. Furino, W. Gilbert, E. Teske, I. VanderBurgh, D. Younger, F. Zorzitto
 1. (a) Find the complete integer solution to the Diophantine equation