Consider the statement: For any numbers a and b, if a + b is odd, then either a or b is odd. First, give a valid proof of the statement using proof by contrapositive. Drag 3 of the statements below to the right column. Statements to choose from: Your Proof: Put chosen statements in order in this column. Therefore a + b is even. Let a and b be integers and assume both are even. Let a and b be integers and assume that a + b is odd but a and b are both even. But then a + b is both even and odd, a contradiction. The sum of two even integers must also be even. Let a and b be integers and assume that if a + b is odd, then either a or bis odd. Let a and b be integers and assume a + b is odd.
Consider the statement: For any numbers a and b, if a + b is odd, then either a or b is odd. First, give a valid proof of the statement using proof by contrapositive. Drag 3 of the statements below to the right column. Statements to choose from: Your Proof: Put chosen statements in order in this column. Therefore a + b is even. Let a and b be integers and assume both are even. Let a and b be integers and assume that a + b is odd but a and b are both even. But then a + b is both even and odd, a contradiction. The sum of two even integers must also be even. Let a and b be integers and assume that if a + b is odd, then either a or bis odd. Let a and b be integers and assume a + b 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:Now prove the statement using a proof by contradiction.
Statements to choose from:
But then a + b is both even and odd, a
contradiction.
Let a and b be integers and assume
a + b is odd.
Therefore a + b is even.
The sum of two even integers must
also be even.
Let a and b be integers and assume
that if a + b is odd, then either a or bis
odd.
Let a and b be integers and assume
both are even.
Let a and b be integers and assume
that a + b is odd but a and b are both
even.
Your Proof: Put chosen statements in order in this column.
Transcribed Image Text:Consider the statement:
For any numbers a and b, if a + b is odd, then either a or b is odd.
First, give a valid proof of the statement using proof by contrapositive. Drag 3 of the statements below to the right column.
Statements to choose from:
Your Proof: Put chosen statements in order in this column.
Therefore a + b is even.
Let a and b be integers and assume
both are even.
Let a and b be integers and assume
that a + b is odd but a and b are both
even.
But then a + b is both even and odd, a
contradiction.
The sum of two even integers must
also be even.
Let a and b be integers and assume
that if a + b is odd, then either a or bis
odd.
Let a and b be integers and assume
a + b is odd.
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