@xxkazamaxx,
Valid Argument - The premises logically guarantee the conclusion.
Sound Argument - The premises are both true and logically guarantee the conclusion.
Tautology - Being true by definition
Contradiction - Having two mutually exclusive properties.
Examples:
VA - All 'a' is 'b'. All 'b' is 'c'. All 'a' is 'c'. Any argument in this form will be logically valid. All gold is yellow. All that is yellow is Mustard. All gold is Mustard. This is a valid argument because of the form it takes, however it fails to be sound because the premises are not true.
SA - All men die. I am a man. I will die. This is valid because if the premises are true, the conclusions must be true. It is sound because the premises are true.
T - All bachelors are men. To be a bachelor is to be an unmarried man, thus it is definitionally true.
C - I am running and not running (easy) -OR- I am running and walking (harder). The easy form of C is to be both something and its negation. The harder form is mutual exclusivity (which includes the easy form). To be red and green is not a contradiction, but to be completely red and completely green is a contradiction.
Now to your questions.
1) I agree. In order to think one must exist in some respect, so long as it is true that I am thinking, I must exist therefore the argument is valid. I am in fact thinking, so the argument is sound.
2) I disagree. In order to cry (just like in number 1) one must exist (this premise is simply suppressed, or not listed). Therefore as long as Alice is in fact crying, she does exist.
3) I agree. The second premise is irrelevant to the conclusion, however, this doesn't matter. So long as your premises are true, the conclusion must be true. In this case the premises are true, so this is valid and sound
4) I agree. If the premises were true, the conclusion would be as well, however, the premises are not all true, therefore valid and unsound is correct.
5) I disagree. Neither premise has anything to do with the conclusion, therefor the argument cannot be valid. validity is a condition of soundness, therefore the argument is neither valid nor sound.
6)I agree as I explained above, soundness depends on validity, so an invalid argument is never sound.
7)Meaning. To be a stag means, in part, to be a deer, therefore the meaning of the words is what results in the truth of the statement (think back to tautology, this is reliant on definition, if the definition changed, the argument would also change).
8) Form. This is the equivalent of Bambi is male and Bambi is a deer, therefore Bambi is a deer. This is different because the definition of deer is irrelevant. No matter how you define deer this will be true.
9) I agree by definition of Tautology.
10)Neither. The reason being that, even though the meanings of 'being wrong' and 'being mistaken' are the same, the object they take in context is not the same. Once this person thought they were wrong about something, but they were mistaken in thinking that. (If however a person was wrong but was mistaken about being wrong, it becomes a contradiction, because that would mean that they were both wrong and not wrong about the same thing.)
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