80-110 The Nature of Mathematical Reasoning

Thursday, April 5, 2001

Quiz 8


    Name: _______________________________
 

  1. What is a propositional formula of propositional logic? (2 points)

  2. 1. Variables: X, Y, Z, ...
    2. If A and B are propositional formulas, so are not A, A v B, A & B, A -> B.< 3. Nothing else is.br> This is a recursive definition. (Lecture).

     
     

  3. 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)

  4. B  & B  C
    ----- & Elim
       B         B --> A
    ---------------------- ->ELim (Modus Ponens)
    A

     
     

  5. Determine (using a truth table) whether the propositional formula `( A v B ) --> A' is a tautology or not. (4 points)

  6. A  B  | A v B -> A
    ----+-----------
    T  T  |   T     T
    T  F  |   T     T
    F  T  |   T     F
    F  F  |   F     T

    Since the colum under the arrow is not completely T, the formula is not a tautology. (Lecture).