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Unformatted text preview: MATH 109 Assignment 3 Due: 4/18/11 #7.2 (i) Counterexample: This is the statement that if m Z + then { n Z + : m n } = Z + . When m = 2, we have 1 / { n Z + : 2 n } so the set does not equal Z + . (iii) Proof. This is the statement that if m Z + then the set { n Z + : m n } is nonempty. Since m { n Z + : m n } , we see that the statement is true for all integers m Z + . (v) Proof. This is the statement that if n Z + then the set { m Z + : m n } is nonempty. Since n { m Z + : m n } , we see that the statement is true for all integers n Z + . #7.4 (iii) Proof. This is the statement that if x R then the set { y R : xy = 0 } is nonempty. Since x 0 = 0, we see that 0 { y R : xy = 0 } , and hence the set is nonempty. (iv) Proof. This is the statement that the set { y R : x R , xy = 0 } is nonempty....
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 Spring '06
 Knutson
 Math

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