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).
     
     

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


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

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


    4.   not A
       :
       :
    Contradiction
    ---------
      A

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

  4. When is an axiom system consistent?


    5. 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)
     
     

  5. When is an axiom system independent?


    6. 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)