P2.6.7 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 x likes walks, T(x) means dog x is a terrier, R(x) means dog x is a Rottweiler, and S(x, y) means dog x is smaller than dog y" or equivalently dog y is larger than dog x. 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