Determine whether the following statements are true or false. Prove the statements directly from the definition...

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Determine whether the following statements are true or false. Prove the statements directly from the definition if they are true, or give counterexamples if they are false. (a) For all integers a, b and c if a band ale then a (2b- 3c). (b) The sum of any three consecutive integers is divisible by 3. (c) For all integers a and n, if a n and a Determine whether the following statements are true or false. Prove the statements directly from the definition if they are true, or give counterexamples if they are false. (a) For all integers a, b and c if a band ale then a (2b- 3c). (b) The sum of any three consecutive integers is divisible by 3. (c) For all integers a and n, if a n and a

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