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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please answer the following questions.
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
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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