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Unformatted text preview: CS 1050 B: Construction Proofs January 25, 2007 Solutions to Homework 1 Lecturer: Sasha Boldyreva Problem 1.1, 4 points. (There was a typo here.) Prove that the proposition if it is not possible to solve the problem, then it is possible to solve it is equivalent to it is possible to solve the problem. Both propositions have the same truth values, regardless of whether it is not possible to solve the problem is true or false. That is, both are true when it is not possible to solve the problem is true and both are false when it is not possible to solve the problem is false. Hence a bi-implication is going to be a tautology. Problem 1.2, 9 points. Write the converse and contrapositive of each statement: a) If the hose is 60 ft long, then the hose will reach the tomatoes. Converse: If the hose will reach the tomatoes, then the hose is 60 ft long. Contrapositive: If the hose will not reach the tomatoes, then the hose is not 60 ft long....
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- Spring '05