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.
- Spring '08