Determine whether the following relation is reflexive, symmetric, antisymmetric and/or transitive. (x, y) ∈ R if x ≥ y, where R is the set of positive integers.
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Let us determine whether the relation if is reflexive, symmetric, antisymmetric and/or transitive.
Since for each positive integer we conclude that the relation is reflexive.
Taking into account that but we conclude that the relation is not symmetric.
If and then and It follows that and hence We conclude that the relation is antisymmetric.
Since and imply and we conclude that , and thus It follows that and thus the relation is transitive.