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1. Decide whether each statement is true or false. Prove your answer (i.e. prove that it...

1. Decide whether each statement is true or false. Prove your answer (i.e. prove that it is true or prove that it is false.)

(a) There exists a nonzero integer α such that α · β is an integer for every rational number β.

(b) For every rational number β, there exists a nonzero integer α such that α · β is an integer.

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