Let R be a relation on the set N of natural numbers defined by nRm Û n is a factor of m (i.e., n|m). Then R is
Question
Let R be a relation on the set N of natural numbers defined by nRm n is a factor of m (i.e., n|m). Then R is
Solution
The relation R is reflexive, antisymmetric and transitive.
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Reflexive: A relation R on a set A is said to be reflexive if every element is related to itself. In this case, every natural number n is a factor of itself. Hence, the relation R is reflexive.
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Antisymmetric: A relation R on a set A is said to be antisymmetric if for any two elements a and b in A, if a is related to b and b is related to a, then a must be equal to b. In this case, if n is a factor of m and m is a factor of n, then n must be equal to m. Hence, the relation R is antisymmetric.
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Transitive: A relation R on a set A is said to be transitive if for any three elements a, b, and c in A, if a is related to b and b is related to c, then a must be related to c. In this case, if n is a factor of m and m is a factor of p, then n is a factor of p. Hence, the relation R is transitive.
Therefore, the relation R is reflexive, antisymmetric, and transitive.
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