hw05 - (b Give an interpretation with a ﬁnite domain...

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Spring-2011 CMSC 250: Homework 5 Due: Wed Mar 2, 2011 NOTE: Due AT THE BEGINNING of Recitation! COURSE WEBSITE: http://www.cs.umd.edu/ gasarch/250/S11.html (NOTE- there is a Tilda before gasarch. It may be easier to get to the course website via the dept webpage (go to class webpages) or gasarch’s homepage (it will be obvious).) 1. (0 points) What is your name? Write it clearly. Staple your HW. 2. (25 points) Simplify the following formula ¬ ( x )( y )[ ¬ R ( x, y ) ( Q ( x, y ) ∨ ¬ S ( x, y ))] . 3. (30 points) In this problem the only domains we allow in the answers are subsets of R . Consider the sentence ( x )( y )[ L ( x, y ) ∧ ¬ S ( x )] . (a) Give an interpretation with a ﬁnite domain where the sentence is true.
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Unformatted text preview: (b) Give an interpretation with a ﬁnite domain where the sentence is false. (c) Give an interpretation with an inﬁnite domain where the sentence is true. 4. (20 points) Show that for every natural number x with 20 ≤ x ≤ 30 CAN be written as the sum of ≤ 8 cubes except for 23 which requires 9 cubes. (You will need to PROVE that 23 cannot be written as the sum of 8 cubes.) 5. (20 points) We call the set of all numbers of the form a + b √ 2 where a, b ∈ Z the CLYDEAN INTEGERS. Show that the product of two CLYDEAN integers is a CLYDEAN integer. 1...
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This note was uploaded on 12/04/2011 for the course CMSC 250 taught by Professor Staff during the Spring '08 term at Maryland.

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