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Each of the following defines a relation on N: x is greater than y, x, y ∈ N Determine whether above relation is reflexive, symmetric and transitive. Each of the following defines a relation on N: x is greater than y, x, y ∈ N Determine whether above relation is reflexive, symmetric and transitive.
Dear StudentGiven,x is greater than y; where x, y∈NIf (x, x)∈R, then x > x, which is not true for any x∈N.so, R is not reflexive.Let (x, y)∈R⇒xRy⇒x>ySo, y > x is not true for any x, y∈NSo, R is not symmetric.Let xRy and yRz⇒x > y and y > z⇒x>z⇒xRzSo, R is transitive.Thanks
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