Assume the R is a relation on a set A, aRb is partially ordered such that a and b are _____________ans.transitivesymmetricreflexive and transitivereflexive 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.transitivesymmetricreflexive and transitivereflexive 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 aRb is partially ordered, then a and b are related in a way that satisfies certain conditions.
In a partially ordered set, the relation R is reflexive, antisymmetric, and transitive.
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Reflexive: This means that every element is related to itself. In other words, for all a in A, aRa holds true.
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Antisymmetric: This means that if a is related to b and b is related to a, then a and b must be the same element. In other words, for all a, b in A, if aRb and bRa, then a = b.
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Transitive: This means that if a is related to b and b is related to c, then a is also related to c. In other words, for all a, b, c in A, if aRb and bRc, then aRc.
So, in the context of a partially ordered set, a and b are elements that satisfy these conditions.
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