Assume the R is a relation on a set A, aRb is partially ordered such t...
A partially ordered relation refers to one which is Reflexive, Transitive and Antisymmetric.
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Assume the R is a relation on a set A, aRb is partially ordered such t...
Explanation:
The given question assumes that R is a relation on a set A, and aRb is partially ordered. In a partially ordered relation, there are three properties that need to be satisfied: reflexivity, transitivity, and antisymmetry. Let's analyze each property and see which options are correct.
Reflexivity:
Reflexivity means that every element in the set A is related to itself. In other words, for every element a in A, aRa should hold true. This property ensures that the relation is reflexive.
Transitivity:
Transitivity means that if a is related to b and b is related to c, then a should also be related to c. In other words, if aRb and bRc, then aRc should hold true. This property ensures that the relation is transitive.
Symmetry:
Symmetry means that if a is related to b, then b should also be related to a. In other words, if aRb, then bRa should hold true. This property ensures that the relation is symmetric.
Answer:
Based on the given information, we know that the relation aRb is partially ordered. From the properties of reflexivity and transitivity discussed above, we can conclude that the correct answer is option 'D' - the relation aRb is reflexive and transitive.
Explanation of options:
a) Reflexive: This property is satisfied in a partially ordered relation.
b) Transitive: This property is satisfied in a partially ordered relation.
c) Symmetric: Symmetry is not a property of a partially ordered relation, so this option is incorrect.
d) Reflexive and Transitive: This option is correct because reflexivity and transitivity are properties of a partially ordered relation.
In summary, a partially ordered relation, denoted by aRb, is reflexive and transitive.
Assume the R is a relation on a set A, aRb is partially ordered such t...
D
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