Tutorial Contents Tutorial Three: Propositional Calculus: Tableaux - The Sentence Tableaux Rules - Testing Arguments for Validity - Sequents - Syntactic Sequents - Semantic Sequents - Soundness and Completeness - Correctness of Sequents and Validity of Arguments More Tutorials One Two Four Five Six Seven

## 1.

Give two translations of each of the following, one using a universal quantifier, and one using an existential quantifier. There are a number of alternative, but equivalent, correct answers. If your answer is different from those given, it may still be right. (Take your domain of quantification to be everything.)
(i) All men are human
(ii) No women like John
(iii) [John likes some women
(iv) Some woman likes John
(v) Only women like John.
(vi) Everyone is a man or a woman.
(vii) Some humans are not men.
(viii)  If someone is a woman, she likes John.

## 2.

Give two translations of each of the following, one using a universal quantifier, and one using an existential quantifier. This time take your domain to be humans.
(i) Everyone is a woman or a man.
(ii) Some humans are not men