Assume the R is a relation on a set A, aRb is partially ordered such that a and b are _____________ ans. reflexive transitive reflexive and transitive symmetric
Question
Assume the R is a relation on a set A, aRb is partially ordered such that a and b are _____________ ans. reflexive
transitive
reflexive and transitive
symmetric
Solution
The correct answer is "reflexive and transitive".
In a partially ordered set (also known as a poset), the relation R is reflexive, antisymmetric, and transitive.
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Reflexive: This means for every element 'a' in set A, the relation aRa holds true. In simpler terms, every element is related to itself.
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Transitive: This means if aRb and bRc, then aRc. In simpler terms, if an element 'a' is related to an element 'b', and 'b' is related to an element 'c', then 'a' is also related to 'c'.
The relation is not necessarily symmetric in a poset. Symmetric means if aRb then bRa, which is not required in a partially ordered set.
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