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Order 7 of the following sentences so that they form a logical proof by contrapositive of the statement: Choose from these sentences: 5x + 17 = 2(5k+8) +1 Then a miracle occurred. 5x + 17 = 5(2k) + 17 = 10k +16+1 Suppose a is an integer that is not odd. 5x + 17 is odd is even. 5x + 17 = 2j+ 1 for some integer j 5x + 17 is even Suppose 5x + 17 is not even. Ek such that a = 2k Your Proof: Væ€Z, 5x + 17 even ⇒ x is odd

Order 7 of the following sentences so that they form a logical proof by contrapositive of the statement: Choose from these sentences: 5x + 17 = 2(5k+8) +1 Then a miracle occurred. 5x + 17 = 5(2k) + 17 = 10k +16+1 Suppose a is an integer that is not odd. 5x + 17 is odd is even. 5x + 17 = 2j+ 1 for some integer j 5x + 17 is even Suppose 5x + 17 is not even. Ek such that a = 2k Your Proof: Væ€Z, 5x + 17 even ⇒ x is odd

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.1: Real Numbers
Problem 38E
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Order 7 of the following sentences so that they form a logical proof by contrapositive of the statement: Choose from these sentences: 5x + 17 = 2(5k+8) +1 Then a miracle occurred. 5x + 17 = 5(2k) + 17 = 10k +16+1 Suppose a is an integer that is not odd. 5x + 17 is odd is even. 5x + 17 = 2j+ 1 for some integer j 5x + 17 is even Suppose 5x + 17 is not even. Ek such that a = 2k Your Proof: Væ€Z, 5x + 17 even ⇒ x is odd
Transcribed Image Text:Order 7 of the following sentences so that they form a logical proof by contrapositive of the statement: Choose from these sentences: 5x + 17 = 2(5k+8) +1 Then a miracle occurred. 5x + 17 = 5(2k) + 17 = 10k +16+1 Suppose a is an integer that is not odd. 5x + 17 is odd is even. 5x + 17 = 2j+ 1 for some integer j 5x + 17 is even Suppose 5x + 17 is not even. Ek such that a = 2k Your Proof: Væ€Z, 5x + 17 even ⇒ x is odd
Below are three statements together with a possible first line of a proof of that statement. In each case, say whether the first line is the start of a direct proof, a proof by contrapositive, or a proof by contradiction. ? 1. Statement: Every three digit number has a sum of digits at most 27. First line: Assume there is some three digit number n whose sume of digits is more than 27. ? First line: Let n be an integer, and assume n is prime. ✓2. Statement: For any integer n, if n is prime, then n is solitary 3. Statement: For any triangle, the sum of the interior angles is 180 degrees. First line: Consider a plane figure and assume that the sum of the interior angles is not 180 degrees.
Transcribed Image Text:Below are three statements together with a possible first line of a proof of that statement. In each case, say whether the first line is the start of a direct proof, a proof by contrapositive, or a proof by contradiction. ? 1. Statement: Every three digit number has a sum of digits at most 27. First line: Assume there is some three digit number n whose sume of digits is more than 27. ? First line: Let n be an integer, and assume n is prime. ✓2. Statement: For any integer n, if n is prime, then n is solitary 3. Statement: For any triangle, the sum of the interior angles is 180 degrees. First line: Consider a plane figure and assume that the sum of the interior angles is not 180 degrees.
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