HW2 - x< y(true when x is less than y using the operators...

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EECS 203: DISCRETE MATHEMATICS Homework 2 Due Thursday, September 20 at 4pm Put your name and discussion section number (not the meeting time) on the first page of your homework. Submit your homework to (a) CTools, as a PDF file, or (b) the drop box marked “EECS 203” in room EECS 2420. If neither (a) nor (b) is possible please turn in your homework at one of the discussion sections. 1. (10) Chapter 1.4, Problem 10 2. (6) Express “Every even number greater than 2 is the sum of two primes” as a quantified formula. Your formula can make use of logical operators and quantifiers ( , , , , ¬ , . . . ), addition, multiplication, and the predicate x = y which is true if x and y are equal. To start off, figure out how to express useful predicates like Even( x ) (true when x is an even number) and
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Unformatted text preview: x < y (true when x is less than y ) using the operators given above. That is, don’t assume you have a predicate Even( x ) — show how to build it from the tools you have. What should the domain of discourse be? 3. (6) Express “There are infinitely many primes” as a quantified formula. Use the same repertoire of operators from the previous question. (There is no direct translation of “infinitely many” in predicate logic so you’ll need to express this using quantifiers.) 4. (6) If n and n +2 are both primes they are called twin primes . For example, 17 and 19 are twin primes. Express “There are a finite number of twin primes” using the same repertoire as above. 5. (4) Chapter 1.5, Problem 24 1...
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