Assume the R is a relation on a set A, aRb is partially ordered such that a and b are _____________ans.reflexive and transitivetransitivereflexivesymmetric Previous Marked for Review Next
Question
Assume the R is a relation on a set A, aRb is partially ordered such that a and b are _____________ans.reflexive and transitivetransitivereflexivesymmetric Previous Marked for Review Next
Solution
The question seems to be incomplete. However, based on the given information, if R is a relation on a set A and is partially ordered, then it must satisfy three properties: reflexivity, antisymmetry, and transitivity.
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Reflexivity: For every element 'a' in set A, the relation aRa must hold true. This means every element is related to itself.
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Antisymmetry: For any two different elements 'a' and 'b' in set A, if aRb and bRa, then a must be equal to b. This means that the relation can't be symmetric for two different elements.
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Transitivity: For any three elements 'a', 'b', and 'c' in set A, if aRb and bRc, then aRc must also hold true. This means if the first element is related to the second, and the second is related to the third, then the first element is also related to the third.
So, in the context of a partially ordered set, the elements 'a' and 'b' are related in a way that is reflexive and transitive, but not necessarily symmetric.
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