Show that the following is a valid argument: All animals when happy, dance. All animals that don’t happy, cry. All crying animals do not eat food. Tommy is not a dancing animal. Therefore, Tommy does not eat food Hint: Needed Predicates H(?) = "? happy" D (?) = "? dance " ? (?) = "? cry " F(?) = "? eat food"

I only need help with the last 3

Let D be a set of dogs including the particular dogs Cardie (c) and Duncan (d). Define the following predicates on D: W(x) means "dog a likes walks", T(x) means “dog æ is a terrier", R(x) means "dog x is a Rottweiler", and S(x, y) means "dog a is smaller than dog y" or equivalently “dog y is larger than dog r". Using the first five of the statements below, prove the last statement using quantifier rules. (Translate the statements into symbolic ones before you start.) • Duncan is a terrier. • All terriers are smaller than Cardie. • Cardie is smaller than some Rottweiler. • If a first dog is smaller than a second dog, and the second is smaller than a third dog, then the first dog is smaller than the third. • All dogs like walks. • There is a Rottweiler who is larger than some terrier who likes walks.

1. Use resolution to determine if the following arguments are valid. Use the predicates suggested.