Order 9 of the following sentences so that they form a logical proof by contradiction of the statement: If the square of an integer is odd then the original integer is also odd If the square of an integer is odd then the original integer is also odd. 1) ∃k ∈ Z such that r^2 =2j 2) r^2=4k^2 3) Suppose that r is an integer such that r^2 is even. 4) Suppose r is even. 5) r^2 is even. 6) ∃k ∈ Z such that r =2k 7) So r^2 is odd and r^2 is even. 8) Suppose r is odd. 9) ∃j ∈ Z such that r = 2k + 1. 10) Let r ∈ Z such that r^2 is odd. 11) Therefore, r is odd 12) Presume the given statement is incorrect
Order 9 of the following sentences so that they form a logical proof by contradiction of the statement: If the square of an integer is odd then the original integer is also odd If the square of an integer is odd then the original integer is also odd. 1) ∃k ∈ Z such that r^2 =2j 2) r^2=4k^2 3) Suppose that r is an integer such that r^2 is even. 4) Suppose r is even. 5) r^2 is even. 6) ∃k ∈ Z such that r =2k 7) So r^2 is odd and r^2 is even. 8) Suppose r is odd. 9) ∃j ∈ Z such that r = 2k + 1. 10) Let r ∈ Z such that r^2 is odd. 11) Therefore, r is odd 12) Presume the given statement is incorrect
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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Order 9 of the following sentences so that they form a logical proof by contradiction of the statement: If the square of an integer is odd then the original integer is also odd
If the square of an integer is odd then the original integer is also odd.
1) ∃k ∈ Z such that r^2 =2j
2) r^2=4k^2
3) Suppose that r is an integer such that r^2 is even.
4) Suppose r is even.
5) r^2 is even.
6) ∃k ∈ Z such that r =2k
7) So r^2 is odd and r^2 is even.
8) Suppose r is odd.
9) ∃j ∈ Z such that r = 2k + 1.
10) Let r ∈ Z such that r^2 is odd.
11) Therefore, r is odd
12) Presume the given statement is incorrect
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