practice1 - EECS 203 Exam 1 Practice Problems These are...

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Unformatted text preview: EECS 203 Exam 1 Practice Problems These are some problems to help you study for the exam. They are not meant to simulate an exam, although some of the problems are similar in scope and difficulty to actual exam problems. Other problems may be a little harder/longer than actual exam problems, but these should still be good practice. Please also be aware that not all topics covered so far are represented in the problems below. 1. Section 1.1, problems 11 c and e. 2. Show that [( p q ) ( p r ) ( q r )] r is a tautology without using truth tables. You may use the equivalences in Tables 6-9 of 1.2, and the tautologies in Table 1 of 1.5. 3. The domain for this problem is Z + , the positive integers. A positive integer n is said to be composite if there exist positive integers a &gt; 1 and b &gt; 1 such that n = ab . Consider the following statement: The product of composite integers is composite. a. Express this statement about natural numbers using quantifiers, logical operators, and...
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