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Question
The following defines a relation on N:
x + y = 10, x, y ∈ N
Determine which of the above relations are reflexive, symmetric and transitive.
Solution
x + y = 10; x, y ∈ N
Thus,
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
Therefore, R is not transitive.
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