M325K_HW05_Soln - M325K Section 3.2 HW 05 - Solutions to...

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M325K HW 05 - Solutions to Graded Questions (Out of 25 points) Section 3.2 10. (4pts) Since m and n are integers, n m 12 5 + and n 4 are both integers (sums and products of integers are integers). Also since 0 n , we have 0 4 n . Thus n n m 4 12 5 + is a quotient of integers with a nonzero denominator. Hence, it is rational. 22. (4pts) True. Proof. Suppose k is any even integer and m is any odd integer. Then 2 + k is even by property 1 on p.145. Also 2 ) 2 ( + k is even because it is product of two even integers (again by property 1). Since m is odd, 1 m is even by property 2. Thus 2 ) 1 ( m is even by property 1 because it is a product of two even integers. Finally 2 2 ) 1 ( ) 2 ( + m k is even because it is a difference of two even integers (this is property 1). 35. (3pts) This incorrect “proof” begs the question by assuming what is to be proved. Namely, the forth sentence claims that s r + is a fraction because it is a sum of two fractions. But this is a restatement
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M325K_HW05_Soln - M325K Section 3.2 HW 05 - Solutions to...

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