Write in symbols the following argument and analyze its validity: I will fail this test if I don't study hard. If I fail this test, they won't give me a car. Or they give me a coal or a car. They don't give me a coal. Therefore, I study a lot. To consider: E: I study a lot. A: I will fail this exam A: I am given a car C: I am given coal

Write in symbols the following argument and analyze its validity: I will fail this test if I don't study hard. If I fail this test, they won't give me a car. Or they give me a coal or a car. They don't give me a coal. Therefore, I study a lot. To consider: E: I study a lot. A: I will fail this exam A: I am given a car C: I am given coal

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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Question

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Write in symbols the following argument and analyze its validity:

I will fail this test if I don't study hard. If I fail this test, they won't give me a car. Or they give me a coal or a car. They don't give me a coal. Therefore, I study a lot.

To consider:

E: I study a lot. A: I will fail this exam A: I am given a car C: I am given coal

R → ¬E
R → ¬A
a.
CV A
.. E
Invälid
R → ¬E
R → ¬A
b.
C V A
.. E
Valid
¬E → R
R → ¬A
C V A
C.
¬C
... E
Invalid
¬E → R
R → ¬A
d.
CV A
¬C
.. E
Válid

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