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(12 points) Use a direct proof technique to prove the following theor.pdf

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mdualudin007

This document contains three mathematical proofs: (1) Any octal number ending in 00 or 40 is divisible by 32. (2) The sum of the cubes of any three consecutive odd integers is divisible by 6. (3) For any sets A, B, C contained in a universal set U, (AB)C = (AC)(BC).

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(12 points) Use a direct proof technique to prove the following theorems: (a) (4 points) For any octal (base-8) string with at least two digits representing unsigned integers, if the last two digits are 00 or 40 , then the number is divisible by 32. (b) (4 points) For any three consecutive odd integers a,b, and c,a3+b3+c33 is divisible by 6 . (c) (4 points) The sets A,B, and C are arbitrary subsets of some universal set U. Prove that (AB)C=(AC)(BC).

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