Express the following argument symbolically, and then prove, using the style of proof , that the 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. (Use h for Ralph does his homework, s for Ralph feels sick, p for Ralph goes to the party, l for Ralph stays up late, and e for Ralph eats too much.)
Warning: You will probably want to use the rule of Simpli?cation at some point in your proof. You need to be careful with that rule! In plain English, the rule says that if you know p and q is true, then you can conclude p is true. But watch out: if p∧q is part of a larger proposition, you can not replace p∧q with p. For example, consider the proposition If I bet $1000 on My Pony and My Pony wins the race, then I will be rich. Obviously it is not valid to say, by Simpli?cation, If I bet $1000 on My Pony, then I will be rich. So, be careful using Simpli?cation.