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Define a relation R on the set Z of all integers as follows: For all m, n elements of Z, mRn if and only if?

ever prime factor of m is a prime factor of n. Is R a partial order relation? prove or give a counter example.

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  • 9 years ago
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    No. 4R2 and 2R4 but 2 =/= 4.

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  • 9 years ago

    No: R isn't antisymmetric. -2 R 2 and 2 R -2 but 2 ≠ -2.

    Edit: good point: R isn't a partial order on N either. Can't believe I missed that... Serves me right for opening my mouth without checking I suppose.

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