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Analysing Arguments: Truth, validity, congency

1. I'm having difficulty analyzing arguments-identifying, supplying missing premises for inductive and deductive arguments, diagramming, reconstructing and listing claims and diagramming. For eg.

Number must be either infinite or finite. But it cannot be infinite. An infinite number is neither odd nor even, but numbers are always odd or even.

How would I list the claims for a passage like the above, diagram it or symbolize it using propositional logic?

2. I'm not sure how to supply missing premises, diagram or determine if an argument is valid or invalid. For eg.

Radioactive elements disintegrate and eventually turn into lead. If matter has always existed there should be no radioactive elements left. The presence of uranium and other radioactive elements is scientific proof that matter has not always existed.

3. How would I diagram an argument like this?

1. q v s
2. ~q
3. s
4. y -> ~s
5. ~y
6. y v (g & h)
7. g & h

4. How would I reconstruct an argument for something like this?

Smokers should be allowed to smoke only in private where it does not offend anyone else. Would any smoker walk into a restaurant and start eating half-chewed food on someone's plate, or drink a glass of water that previously held someone's teeth? Probably not, yet they expect non-smokers to inhale smoke from the recesses of their lungs! My privilege and right is to choose a clean and healthy life without interference.

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Solution Summary

The solution is a collection of materials and organized academic advise in Philosophy (Critical Thinking & Reasoning) to help the student take on a complicated passage to arrive at logical claims using diagrams, symbols and propositional logic. The solution tackles proposing validity and invalidity of passages and claims using easy to understand materials to concisely explain deduction and induction, validity, invalidity, cogency and uncongency; translating arguments as well as providing a testing mechanism via the use of truth tables.