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
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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
Transcribed Image Text: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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