Assume the R is a relation on a set A, aRb is partially ordered such that a and b are _____________ans.symmetricreflexivereflexive and transitivetransitive
Question
Assume the R is a relation on a set A, aRb is partially ordered such that a and b are _____________
- ans.
- symmetric
- reflexive
- reflexive and transitive
- transitive
Solution
The question seems to be asking for the properties of a and b in a partially ordered set (poset). In a poset, the relation R is reflexive, antisymmetric, and transitive.
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Reflexive: For every element 'a' in set A, the relation aRa holds true. This means every element is related to itself.
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Antisymmetric: For all 'a' and 'b' in set A, if aRb and bRa, then a = b. This means that the only way for both aRb and bRa to hold is if a and b are the same element.
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Transitive: For all 'a', 'b', and 'c' in set A, if aRb and bRc, then aRc. This means that if 'a' is related to 'b', and 'b' is related to 'c', then 'a' is also related to 'c'.
So, the answer to the question is "reflexive and transitive".
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