a) isn't a valid argument because the conclusion doesn't follow from the two premises. There's a possibility that you could get an without studying hard.
b) is valid.
Check this site for a good explanation of validity.
http://www.jimpryor.net/teaching/vocab/validity.html
We'll be glad to check the rest of your answers.
1. Determine whether the following arguments are valid or invalid. If valid determine whether they are sound. Be sure to explain what validity is and how you determine whether an argument is valid or not. Explain your answers in as much detail as you can. There is no length restriction on your answer; make it as long as necessary to answer the question in the required detail.
a.) If I study hard I’m sure to get an A in philosophy, but I haven’t studied at all; So I can’t get an A.
b.) If a number is greater than 7 then it is greater than 4. 8 is greater than 7, therefore it is greater than 4.
c.) If I want an A in philosophy I need to study for the exam, since I haven’t studied for the exam that means that I don’t want an A.
d.) No computers can feel pain. The human brain is a computer so no human brains feel pain.
e.) How do I know that Hillary Clinton is a liar? All politicians lie to get ahead and Hillary Clinton is a politician!
f.) If 4 is prime then it is divisible only by 1 and itself. 4 is not prime therefore it is divisible by numbers other than 1 and itself.
g.) Some doctors watch Lost and some people who like Lost are conspiracy theorist so some doctors are conspiracy theorists.
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