Math 2090.03 N (Winter 98-99) TEST 2B Part 1
Friday March 19th, 1999
SOLUTIONS

SURNAME (BLOCK CAPITALS):

INITIALS:

STUDENT NUMBER:

SIGNATURE:

All questions concern our propositional logic tex2html_wrap_inline27 and material covered in Chapter 4 of the course text. The marks for each question are shown in brackets. You may NOT use inference rule/Metatheorem MON-AMON or inference rule/Metatheorem MODUS-PONENS anywhere on the test.

All axioms, allowed Metatheorems from Chapters 3 and 4, and lower numbered theorems may be used in the proof of a higher numbered theorem.

The 4th page has been left blank for working, please indicate if there is part of your test there that needs marking. To ensure your paper is graded correctly please underline which part of a sentence a theorem is being applied to.


  1. Give a bullet proof, using Proof Method 4.1, that tex2html_wrap_inline29. Do not use anything beyond tex2html_wrap_inline31. (10)

    SOLUTION

    tex2html_wrap_inline33

  2. Give a bullet proof, using the Deduction Theorem, that
    displaymath35
    Do not use anything beyond tex2html_wrap_inline37. You may wish to turn the consequent into a sentence which we can deduce from our assumptions by one application of a basic inference rule to be a theorem. Show this by circling the sentence and stating by which inference rule it is a theorem.(10)

    SOLUTION

    Assume tex2html_wrap_inline39.

    tex2html_wrap_inline41

    Since tex2html_wrap_inline43 and tex2html_wrap_inline45 by TRANSITIVITY we get tex2html_wrap_inline47.

  3. Give a bullet proof, using Proof by Cases, that tex2html_wrap_inline49 (tex2html_wrap_inline51). In each case you may wish to transform the whole sentence into a known theorem. (10)

    SOLUTION

    tex2html_wrap_inline53

    tex2html_wrap_inline55





Stephanie-van Willigenburg
Wed Mar 17 14:47:01 EST 1999