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Unformatted text preview: errors have been detected. c) The ﬁle system cannot be backed up if there is a user currently logged in. d) Video on demand can be delivered when there are at least 8 megabytes of memory available and the connection speed is at least 56 kilobits per second. Problem 1.4, 4 points. Explain why an argument of the following form is not valid: (( p → q ) ∧¬ p ) → ¬ q . Problem 1.5, 5 points. Determine whether the following argument is valid. Name the rule of inference or explain the fallacy. Theorem: If n is a real number such that n > 1, then n 2 > 1. Proof: Suppose that n 2 > 1. Then n > 1. Problem 1.6, 18 points. Consider the following theorem: If x is an odd integer, then x +2 is odd. Give (a) a direct proof, (b) a proof by contradiction and (c) a proof by contraposition of this theorem. Problem 1.7, 4 points. Give a proof by cases of the following. All digits have English names consisting of at most 6 letters....
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- Spring '05
- Logic, Lecturer, Sasha Boldyreva