Here are additional questions with answers that you might help you to prepare for the final exam.
Try first to answer the questions by yourself, before you look at
the answers !
Questions regarding the first half of the course are here.
Every syllogism was given a particular name to identify it. Give an
example of such a name that was given to a syllogism.
What is the biggest drawback of Aristotle's theory of syllogisms?
What is the arity of a predicate?
What is the difference between a sentence and a term?
Is (1+1+1) a term in the first order language of arithmetic?
What is a propositional formula of propositional logic? (2 points)
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)
Determine (using a truth table) whether the propositional formula `( A v B ) --> A' is a tautology or not. (4 points)
What is the meaning of the following: "Gamma |= S", where Gamma is a
set of propositional formulas, and S a propositional formula.
What is the difference between propositional logic and
predicate logic?
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?
Name one non-classical logic.
What does a recursive definition consist of?
Who is the founder of modern set theory?
What does ZF stand for?
What does it mean for a function f:A->B to be 1-1 (one-to-one,
injective)?
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 )"?