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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.

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5965 Points
one year ago
Dear Student
Given,
x is greater than y; where x, y∈N
If (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>y
So, y > x is not true for any x, y∈N
So, R is not symmetric.
Let xRy and yRz
⇒x > y and y > z
⇒x>z
⇒xRz
So, R is transitive.

Thanks

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