<p> COT 3100 Quiz #2 Solutions: Rules of Inference 1/19/05</p><p>1) Prove the following, using the rules of inference:</p><p>[ (p  (q  r))  (p  s)  (t  q)  s]  [r  t]</p><p>(Note: There are four premises given above.)</p><p>1. p  s Premise</p><p>2. s Premise</p><p>3. p Rule of Disjunctive Syllogism (with #1,#2)</p><p>4. p  (q  r) Premise</p><p>5. q  r Modus Ponens (with #3, #4)</p><p>6. t  q Premise</p><p>7. t  r Law of Syllogism (with #6,#5)</p><p>8. r  t Contrapositive</p><p>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</p>