Quiz 7 – Critical Thinking                                          April 1, 2003

 

Use your own paper for this quiz. Use your notes if you wish.  PLEASE WRITE LEGIBLY SINCE ILLEGIBLE ANSWERS WILL RECEIVE NO CREDIT.

 

1.  Symbolize the following statements:

 

  1. Either A or B but not both C and D.
    1. (A v B) . ~(C . D)
  2. Neither A nor B if C.
    1. C à ~(A v B)
  3. H on condition that B.
    1. B à H
  4. If either A or B, then both C and D.
    1. (A v B) à (C . D)

 

2.  Are these statements equivalent to each other?  How do you know?

 

  1. (A v B) and ~(~A . ~B).  Yes.  (A v B) is equivalent to ~~(A v B), which is equivalent by DeMorgan’s Theorem to ~(~A . ~B).
  2. (A v B) and (~A à B).  Yes.  (A v B) is equivalent to (~A à B) by application of Double Negation (~~A v B) and use of material implication.
  3. (A . B) and ~(~A v ~B)  Yes.  (A . B) is equivalent to ~~(A . B), and by DeM, this yields ~(~A v ~B).
  4. (A à B) and (~A v B).  Yes.  By material implication.

 

If you did truth tables on each of these, they are tautologies.

 

3.  What is a tautology?  A necessarily true statement.  In truth table terms, all the values under the major connective (the ß> symbol) are true.

 

4.  What is a contingent statement?  A statement that is true under some conditions and false under others.  In a truth table, the major connective yields at least one true substitution and at least one false substitution.