COT 3100 Quiz #2: Rules of Inference 1/19/05

COT 3100 Quiz #2 Solutions: Rules of Inference 1/19/05

1) Prove the following, using the rules of inference:

[ (p  (q  r))  (p  s)  (t  q)  s]  [r  t]

(Note: There are four premises given above.)

1. p  s Premise

2. s Premise

3. p Rule of Disjunctive Syllogism (with #1,#2)

4. p  (q  r) Premise

5. q  r Modus Ponens (with #3, #4)

6. t  q Premise

7. t  r Law of Syllogism (with #6,#5)

8. r  t Contrapositive

2) Provide English expressions to substitute for p, q, r, s and t above that would make a reasonable argument when plugged into the statement proved above. p: My best friend is visiting from out of town q: There is no exam I have to give in class today r: I will take my friend to Disney World s: My best friend called to let me know he can not come to visit t: I gave an exam the last class period