If a number is divisible by 6, then it is divisible by 2 and 3.  If a number is divisible by 2 and 3, then it is divisible by 6. If a number is divisible by 2 and 4, then it is divisible by 8. If a number is divisible by 8, then it is divisible by 2 and 4. A number is divisible by 8 if, and only if, it is divisible by 2 and by 4.

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter1: Introduction To Algebra
Section1.2: Grouping Symbols
Problem 7MRE
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Classify each of the following statements as true or false.

  1. If a number is divisible by 6, then it is divisible by 2 and 3. 

  2. If a number is divisible by 2 and 3, then it is divisible by 6.

  3. If a number is divisible by 2 and 4, then it is divisible by 8.

  4. If a number is divisible by 8, then it is divisible by 2 and 4.

  5. A number is divisible by 8 if, and only if, it is divisible by 2 and by 4.

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