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Question
The following defines a relation on N:
x is greater than y, x, y ∈ N
Determine which of the above relations are reflexive, symmetric and transitive.
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Solution
Given, x is greater than y; x, y ∈ N
If (x, x) ∈ R, then x > x, which is not true for any x ∈ N.
Thus, R is not reflexive.
Let (x, y) ∈ R
⇒ xRy
⇒ x > y
So, y > x is not true for any x, y ∈ N
Hence, R is not symmetric.
Let xRy and yRz
⇒ x > y and y > z
⇒ x > z
⇒ xRz
Hence, R is transitive.
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