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4. Let a and ß be arbitrary statement forms, and consider the following general claim: If a is consistent and a →ß is consistent, then ß is also consistent. Is this general claim true?

4. Let a and ß be arbitrary statement forms, and consider the following general claim: If a is consistent and a →ß is consistent, then ß is also consistent. Is this general claim true?

Advanced Engineering Mathematics
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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4. Let a and ß be arbitrary statement forms, and consider the following general claim: If a is consistent and a →ß is consistent, then ß is also consistent. Is this general claim true? NOTE: You must justify your answer. To establish the truth of a general claim, you must explain (briefly, in a few coherent sentences), on the basis of the relevant definitions, how you know that no matter what statement forms the symbols 'a' and 'B' might be chosen to represent, the claim always comes out true. To establish the falsity of a general claim, all you need do- but do this you must! - is provide a "counterexample" to the general claim. In this context, that means that you need to explicitly exhibit a pair of actual statement forms, indicating which is playing the role of a and which is playing the role of ß, such that when they are substituted into the general claim, the result is a false sentence about these particular statement forms.
Transcribed Image Text:4. Let a and ß be arbitrary statement forms, and consider the following general claim: If a is consistent and a →ß is consistent, then ß is also consistent. Is this general claim true? NOTE: You must justify your answer. To establish the truth of a general claim, you must explain (briefly, in a few coherent sentences), on the basis of the relevant definitions, how you know that no matter what statement forms the symbols 'a' and 'B' might be chosen to represent, the claim always comes out true. To establish the falsity of a general claim, all you need do- but do this you must! - is provide a "counterexample" to the general claim. In this context, that means that you need to explicitly exhibit a pair of actual statement forms, indicating which is playing the role of a and which is playing the role of ß, such that when they are substituted into the general claim, the result is a false sentence about these particular statement forms.
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