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.
- rodolfo riverolLv 69 years agoFavorite Answer
No. 4R2 and 2R4 but 2 =/= 4.
- David ThorstadLv 69 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.