%%% Assignment 7 %%% Out: Mon 12 Nov %%% Due: Mon 19 Nov % % This assignment is to be submitted electronically using Tutch. % Comment out those parts of problems 1,2, and 4 that cannot % be checked by Tutch. % % % 1. Syllogism. % % Prove that the following argument is valid. % % No philosophers are Spartans. % Some Greeks are Spartans. % -------------------------------- % Some Greeks are not philosophers. % % % % 2. Formalization. % % In Huth & Ryan section 2.2, do exercize 6 on p. 102, % and in section 2.3, do exercize 12 on p. 128. % % % % 3. Quantifier Laws. % % Give proofs and terms for the following entailments. % % proof CEa : (A & ?x:t. B(x)) => (?x:t. A & B(x)) = % term CEa : (A & ?x:t. B(x)) => (?x:t. A & B(x)) = % % proof CEb : (?x:t. A & B(x)) => (A & ?x:t. B(x)) = % term CEb : (?x:t. A & B(x)) => (A & ?x:t. B(x)) = % % % proof DUa : (A | !x:t. B(x)) => (!x:t. A | B(x)) = % term DUa : (A | !x:t. B(x)) => (!x:t. A | B(x)) = % % proof DUb : (!x:t. A | B(x)) => (A | !x:t. B(x)) = % term DUb : (!x:t. A | B(x)) => (A | !x:t. B(x)) = % % % % 4. Classical Versus Constructive Validity. % % a. Show that the following entailment is classically valid, % but not constructively so. % % ((!x:t. B(x)) => A) => (?x:t. B(x) => A) % % % b. Give an (informal) interpretation to show that the following % is not even classically valid (and so not constructively). % % (?x:t. B(x) => A) => ((?x:t. B(x)) => A) % % %%%