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# Advanced Math/Logic - True and False

Question
I was doing true and false and these 6 were giving me some issues. I'm very bad at logic, but it's a required course for my major so just trying to get some help to understand it better.

1. Modus Tollens (MT) requires a conditional on it's own line and the negation of the conditional's consequent on another line.

2. If you have a disjunction on its own line and the negation of the right-hand disjunct on another line, then you may use disjunctive syllogism (DS) rule.

3. The statement variables (P and Q) in the form of (DS) may stand for compound statements.

4. In a natural deduction proof, each new line follows by necessity from the lines above.

5. When you are using a natural deduction proof to show that an argument is valid, the last line of your proof should always match the first premise.

6. If you derive the statement C v F from the statement (Z • F) ⊃ (C v F) and from the statement Z • F, then you are using Modus Ponens (MP).

1. True. This is what it is saying.
If P->Q and
~Q then
~P
P->Q is a conditional, with Q the consequent, they are saying Q is false so therefore P must be false too.

2. Is false because a disjunctive statement is P V Q, DS says if you have ~P then Q is true. 2 says ~Q then P is true. These are logically equivalent because if you have in one step P V Q on the next line you can write Q V P and then if you have ~Q you can derive P. The only reason this statement is false is because you need to also have the step Q V P and 2 doesn't state that.

3. This one is tricky but if you go with a compound statement having two or more logic operations in DS the only operation you have is 'or' so I would say false.

4.  True. This is just saying that any statement you make, it must follow from one or more previous statements.

5.  False because a premise is what you get to assume is true, so you can't conclude it.

6.  Think of  Z and F as P and C or V as Q, then you have if P then Q, and P and conclude Q. Is this what Modus Ponens gives you?
If you have a conditional statement P->Q and you have the antecedent P, then you get Q free of charge. You have all of that so true you would be using MP.

I hope this helps you a little in your understanding of logic.

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