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Question
The following defines a relation on N:
x + 4y = 10 x, y ∈ N.
Determine which of the above relations are reflexive, symmetric and transitive.
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Solution
x + 4y = 10; x, y ∈ N
R = {(x, y): x + 4y = 10; x, y ∈ N}
R = {(2, 2), (6, 1)}
It’s clearly seen (1, 1) ∉ R
Hence, R is not symmetric.
(x, y) ∈ R ⇒ x + 4y = 10
And (y, z) ∈ R ⇒ y + 4z = 10
⇒ x – 16z = – 30
⇒ (x, z) ∉ R
Therefore, R is not transitive.
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