Proof Project Writing Assignment Using the "road map" provided during class for the example theorem, prove the theorem "If n is odd, then n+1 is even" in the following ways: 1) Direct proof (Assume p, show q ). 2) Proof by contraposition (Assume ~q, show ~p). 3) Proof by contradiction (Assume p and ~ q, then seek a contradiction). It is important to consider your audience when doing any type of writing. For this assignment, assume you are writing your proofs so that another student in the class who has missed a few lessons can follow your logic and easily understand your proofs. As you read through your proofs, consider the following questions: ● Does each proof align with the traditional proof structure discussed in class? ● Do the ideas flow clearly and logically from one sentence to the next? ● Is there any missing information that would contribute to the clarity of the argument (consider the audience when thinking about this)? ● Is the proof general enough to apply to any odd input (ie, make sure it isn't a "proof" by example)? ● Are there any logical fallacies (affirming the conclusion, using the inverse/converse instead of the contrapositive, etc...)?
Proof Project Writing Assignment
Using the "road map" provided during class for the example theorem, prove the theorem "If n is odd, then n+1 is even" in the following ways:
1) Direct proof (Assume p, show q ).
2) Proof by contraposition (Assume ~q, show ~p).
3) Proof by contradiction (Assume p and ~ q, then seek a contradiction).
It is important to consider your audience when doing any type of writing. For this assignment, assume you are writing your proofs so that another student in the class who has missed a few lessons can follow your logic and easily understand your proofs.
As you read through your proofs, consider the following questions:
● Does each proof align with the traditional proof structure discussed in class?
● Do the ideas flow clearly and logically from one sentence to the next?
● Is there any missing information that would contribute to the clarity of the argument (consider the
audience when thinking about this)?
● Is the proof general enough to apply to any odd input (ie, make sure it isn't a "proof" by example)?
● Are there any logical fallacies (affirming the conclusion, using the inverse/converse instead of the
contrapositive, etc...)?
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