Originally Posted by

**kturf** Prove the following argument is valid.

If Ralph doesn't do his homework or he doesn't feel sick, then he will go to the party and he will stay up late. If he goes to the party, he will eat too much. He didn't eat too much. So Ralph did his homework.

So far I came up with the following:

Let's Set:

H(x): Ralph does his homework

S(x): Ralph feels sick

P(x): Ralph goes to the party

L(x): Ralph stays up late

E(x): Ralph eats too much

Argument:

(¬H(x) v ¬S(x)) → (P(x) ∧ L(x))

P(x) → E(x)

¬E(x)

H(x)

Not positive the above is right or not. But either way - I don't understand how to do the proofs. We can use the following Rules of Inference:

Modus Ponens

Modus Tollens

Hypothetical Syllogism

Addition

Simplification

Conjunction

Disjunctive Syllogism

Help would be much appreciated.