# Questions (2)

Try first to answer the questions by yourself, before you look at the answers !

Questions regarding the first half of the course are here.

1. Every syllogism was given a particular name to identify it. Give an example of such a name that was given to a syllogism.
2. What is the biggest drawback of Aristotle's theory of syllogisms?
3. What is the arity of a predicate?
4. What is the difference between a sentence and a term?
5. Is (1+1+1) a term in the first order language of arithmetic?
6. What is a propositional formula of propositional logic? (2 points)
7. Give a syntactic proof (using the Natural Deduction rules) of "A" from the premises "B --> A" and "B & C". Say what rules you are using. (4 points)
8. Determine (using a truth table) whether the propositional formula `( A v B ) --> A' is a tautology or not. (4 points)
9. What is the meaning of the following: "Gamma |= S", where Gamma is a set of propositional formulas, and S a propositional formula.
10. What is the difference between propositional logic and predicate logic?
11. What does the sentence "there exits x forall y ( x <= y)" mean, if the domain of the bound variables are the natural numbers and "<=" stands for "is less or equal than"? Is the sentence true or false?
12. Name one non-classical logic.
13. What does a recursive definition consist of?
14. Who is the founder of modern set theory?
15. What does ZF stand for?
16. What does it mean for a function f:A->B to be 1-1 (one-to-one, injective)?
17. Which of the following two sentences of predicate logic can be true in a finite domain, and which in an infinite domain of objects: "forall x exists y ( x < y )" and "exists x forall y ( x < y )"?