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Each of the following defines a relation on N: x + y = 10, x, y ∈ N Determine whether above relation is reflexive, symmetric and transitive.

 Each of the following defines a relation on N: 
  x + y = 10, x, y ∈ N
 
Determine  whether above relation is  reflexive, symmetric and transitive.

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5963 Points
2 years ago
Dear Student
x + y = 10; x, y∈N

R = {(x, y); x + y = 10, x, y∈N}
R = {(1, 9), (2, 8), (3, 7), (4, 6), (5, 5), (6, 4), (7, 3), (8, 2), (9, 1)}
It’s clear (1, 1)∉R
So, R is not reflexive.
(x, y)∈R⇒(y, x)∈R
Therefore, R is symmetric.
Now (1, 9)∈R, (9, 1)∈R, but (1, 1)∉R
Thus, R is not transitive.


Thanks

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