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2. When proving a statement of the form "S ," one ef- fective strategy is to use proof by contradiction. Specit- ically, begin with the assumption that there is some ele- ment xe S, and argue that some absurdity results. Try this type of reasoning on the following statements to be proven: (a) (2k+1: ke N} n (4k: ke N} = Ø (b) ((3k+1: ke Z) n (6k+5: ke Z}) = Ø (c) (1(x, y) e R xR : -2x-3 y} n((x, y)e 6 y}) = 0 R x R: x (d) If A C B, then A n B' =0. for the follor.

2. When proving a statement of the form "S ," one ef- fective strategy is to use proof by contradiction. Specit- ically, begin with the assumption that there is some ele- ment xe S, and argue that some absurdity results. Try this type of reasoning on the following statements to be proven: (a) (2k+1: ke N} n (4k: ke N} = Ø (b) ((3k+1: ke Z) n (6k+5: ke Z}) = Ø (c) (1(x, y) e R xR : -2x-3 y} n((x, y)e 6 y}) = 0 R x R: x (d) If A C B, then A n B' =0. for the follor.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 63RE
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2. When proving a statement of the form "S ," one ef- fective strategy is to use proof by contradiction. Specit- ically, begin with the assumption that there is some ele- ment xe S, and argue that some absurdity results. Try this type of reasoning on the following statements to be proven: (a) (2k+1: ke N} n (4k: ke N} = Ø (b) ((3k+1: ke Z) n (6k+5: ke Z}) = Ø
Transcribed Image Text:2. When proving a statement of the form "S ," one ef- fective strategy is to use proof by contradiction. Specit- ically, begin with the assumption that there is some ele- ment xe S, and argue that some absurdity results. Try this type of reasoning on the following statements to be proven: (a) (2k+1: ke N} n (4k: ke N} = Ø (b) ((3k+1: ke Z) n (6k+5: ke Z}) = Ø
(c) (1(x, y) e R xR : -2x-3 y} n((x, y)e 6 y}) = 0 R x R: x (d) If A C B, then A n B' =0. for the follor.
Transcribed Image Text:(c) (1(x, y) e R xR : -2x-3 y} n((x, y)e 6 y}) = 0 R x R: x (d) If A C B, then A n B' =0. for the follor.
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