Answered: Your task is to show that these rules…

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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We introduced some rules of inference that are truth preserving. Here are other rules of inference that
are truth preserving.
1. From a formula ¬G and (F → G), infer ¬F . This is known as modus tollens (Literally Latin for "the
way of taking away or removing")
2. From a formula F and (F → G), infer G. This is known as modus ponens (Literally Latin for "the way
of putting or placing")
3. From a formula (F ∧ G) infer F . Similarly from a formula (F ∧ G) infer G. So from a conjunction
of two formulas you can infer either conjunct. This rule of inference is sometimes called "conjunction
elimination."
Your task is to show that these rules of inference are truth preserving by verifying that the following formulas
are tautologies.
(a) Modus Tollens ((¬G ∧ (F → G)) → ¬F )
(b) Modus Ponens ((F ∧ (F → G)) → G)
(c) Conjunction Elimination I ((F ∧ G) → F )
(d) Conjunction Elimination II ((F ∧ G) → G)

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