2 Name: Write or type solutions on a separate paper. If written, write legibly. 1. Rewrite each statement into a predicate wff with the domain of the whole world. Indicate what each predicate represent. (a) Cats are smarter than dogs.. (b) Some pizzas are round. (c) Only science majors take calculus. (d) Not all balls are tennis balls. 2. Give the English language translations of the following wffs if M (x): x is a man W (x): x is a woman W (x, y): x works for y \u0001 \u0001 \u0002 \u00030 \u0001\u0001 (a) x W (x) y M (y) W (x, y) \u0001 \u0001 \u0001\u0001 (b) x M (x) y W (y) W (x, y) \u0001 \u0001 \u0001\u0001 (c) x M (x) y W (x, y) W (y) \u0001 \u0001 \u0001 (d) x y M (x) W (y, x) W (y) 3. Decide weather each of the following predicate wffs is valid or invalid. If it is valid explain why; and if, it is invalid give an interpreation to justify your answer. \u0001 (a) P (a) x P (x) \u0001 \u0001 \u0001 \u0001 (b) x P (x) x Q(x) x P (x) Q(x) \u0001 \u0001 \u0001 \u0001 (c) x P (x) x Q(x) x P (x) Q(x) \u0001 \u0001 \u0001 \u0001 \u0001 \u0001 (d) x P (x) Q(x) x P (x) Q(x) x P (x) Q(x) 4. Prove or disprove the following predicate wffs is valid using derivation rules. If the predicate wff is invalid, give an interpretation that satisfy your claim. \u0001 \u0001 \u0002 \u0001 \u0001 \u0003 (a) x P (x) Q(x) x P (x) x Q(x) \u0001 \u0001 \u0001 \u0001 (b) x P (x) Q(x) x P (x) x Q(x) \u0001 \u0001 \u0001 \u0001 (c) y Q(x, y) P (x) y Q(x, y) P (x) \u0001 \u0001 \u0001 \u0001 (d) x P (x) Q(x) x Q(x) x Q(x) 5. Write the following verbal argument in predicate form and prove that the argument is valid. Every member of the board comes from industry or government. Everyone from government who has a law degree is in favor of the motion. John is not from industry, but he has a law degree. Therefore, if John is a member of the board, he is in favor of the motion