Math 2090.03 N Assignment 1
due January 29th, 1999

INSTRUCTIONS: This assignment is due January 29th 1999, in class. Groups may hand in a single assignment paper. The maximum group size is 4.

The assignments must have the name and York number of all group members listed at the top of the paper.


  1. Using truth tables show that tex2html_wrap_inline21 is a tautology.

    SOLUTION: tex2html_wrap_inline23

    So since tex2html_wrap_inline21 is T (or true) in all states, it is a tautology.

  2. Fill in the missing details to make the following a full dress proof that tex2html_wrap_inline31.

    SOLUTION:
    eqnarray11

    By Metatheorem which says if tex2html_wrap_inline33 since tex2html_wrap_inline35 and tex2html_wrap_inline37 we have tex2html_wrap_inline39.

    By TRANSITIVITY 4 times tex2html_wrap_inline41 and hence by EQUANIMITY tex2html_wrap_inline31.

  3. Give a full dress proof that tex2html_wrap_inline45. You may use any of the axioms given in Chapter 3.

    SOLUTION:
    eqnarray13

    Now tex2html_wrap_inline47, and tex2html_wrap_inline49 by TRASITIVITY 3 times, and so tex2html_wrap_inline51 by EQUANIMITY.


Stephanie van Willigenburg