# exam1sol - COT 3100 Exam#1 Solutions Lecturer Arup Guha...

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COT 3100 Exam #1 Solutions Lecturer: Arup Guha 9/19/02

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1) (10 pts) Using only the laws of logic, show that the expression below is a tautology. ( (p ¬ p) ( q ¬ ( ¬ q ¬ r) ) ) ( (p ¬ p) ¬ q ) ( (p ¬ p) ( q ¬ ( ¬ q ¬ r) ) ) ( (p ¬ p) ¬ q) ( T ( q ¬ ( ¬ q ¬ r) ) ) ( T ¬ q) (using Inverse Laws twice) ( q ¬ ( ¬ q ¬ r) ) ( ¬ q) (using Identity Laws twice) ( q ( ¬ q) ) ¬ ( ¬ q ¬ r) (using commutative and associative) T ¬ ( ¬ q ¬ r) (using Inverse Law) T (using Domination Law)
2) (15 pts) Consider the following argument: If the Yankees win the pennant, then they will win the World Series. If the Angels win the pennant, then I will make \$1000 on my bet. Either the Yankees or the Angels won the pennant. The Yankees did NOT win the world series, therefore I will make \$1000 on my bet. Assign the four variables below to simple statements in the argument above. p: Yankees win the pennant. q: Yankees win the world series. r: Angels win the pennant. s: I will make \$1000 on my bet State the four premises in terms of these variables. What is the conclusion drawn from these premises? Prove that the conclusion is valid using the rules of inference. Premises:

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exam1sol - COT 3100 Exam#1 Solutions Lecturer Arup Guha...

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