Friday March 19th, 1999

SOLUTIONS

SURNAME (BLOCK CAPITALS):

INITIALS:

STUDENT NUMBER:

SIGNATURE:

All questions concern our propositional logic 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.

- Give a bullet proof, using Proof Method 4.1, that . Do not use anything beyond . (10)
SOLUTION

- Give a bullet proof, using the Deduction Theorem, that

Do not use anything beyond . 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 .

Since and by TRANSITIVITY we get .

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

Wed Mar 17 14:47:01 EST 1999