80-110 The Nature of Mathematical Reasoning

Tuesday, July 18 2000

Quiz 4

Name: _______________________________

1. How are atomic sentences formed in FOL?

2. Atomic sentences are formed by putting a predicate of aritiy n in front of n names (enclosed in parentheses and separated by commas). Atomic sentences are built from the identity predicate, =, using infix notation: the arguments are placed on either side of the predicate. (FOL, page 13).

3. Is (1+1+1) a term in the first order language of arithmetic?

4. No, (1+(1+1)) or ((1+1)+1) would be terms. (FOL, page20).

5. What is the structure of an argument of the form indirect proof?

6.   not A
:
:
---------
A

From the assumption `not A' and the derivation of a contradiction you infer `A'. (Lecture 7/12/00)

7. When is an axiom system consistent?

8. An axiom system is inconsistent if it is possible to prove both a statement and its negation from the axioms. A system is consistent if it is not inconsistent. (Lecture 7/17/00)

9. When is an axiom system independent?

10. An axiom \$A\$ is independent if it cannot be proved from the remaining axioms. An axiom system is independent, if all its axioms are independent from each other. (Lecture 7/17/00)