Deductive logic test

[Sblast]

So if I understood correctly, if the first premise is a contradiction -i.e., something is and it is not simultaneously - then anything goes, basically? Both are true, so you can conclude what follows from either is or is not? But isn't the conclusion still invalid since all chese is Roquefort cheese although all Roquefort cheese isn't moon cheese? And doesn't this go against the law of noncontradiction, that A cannot be both A and not A at the same time?

Yeah, I put it confusingly, without that premise it would be invalid - but it's a premise in the argument regardless - which is always false.
Its falsehood is an implication of the law of noncontradiction (A cannot be both A and not A at the same time). Yes, anything follows, which makes it quite useless and a good reason to introduce the criteria of soundness.

[Herr Abubu]

Yeah, I put it confusingly, without that premise it would be invalid - but it's a premise in the argument regardless - which is always false.
Its falsehood is an implication of the law of noncontradiction (A cannot be both A and not A at the same time). Yes, anything follows, which makes it quite useless and a good reason to introduce the criteria of soundness.

Ok, I think I've understood it now. Quite counterintuitive at first.

[Mortimer]

Given the first premise is a part of the argument, the argument is valid. An argument is valid iff it is not possible for the conclusion to be false if the premises are true. It's impossible for the premises to be true when a contradiction is a premise (since it's always false) - there's no possibility that the premises are true and conclusion false - hence, the argument is valid. It's known as the principle of explosion.

i didnt thought about it like that. i excluded the first sentence because it is a contradiction so i thought it eliminates itself, i took that all cheese is roquefort cheese and that roquefort cheese is moon cheese since all cheese is roquefort cheese therefore the cheese in the moon must be roquefort. but it is interesting. i think you need to study it and learn more about it to know the various techniques

[Lena]

btw, seen much complicated tests, maybe someone could find them and post links here.