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Question
Determine whether the following relation is reflexive, symmetric and transitive:
Relation R in the set A = {1, 2, 3, ..., 13, 14} defined as R = {(x, y) : 3x – y = 0}.
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Solution
A = {1, 2, 3, ..., 13, 14}
R = {(x, y) : 3x – y = 0}
∴ R = {(1, 3), (2, 6), (3, 9), (4, 12)}
R is not reflexive since (1, 1), (2, 2), ..., (14, 14) ∉ R.
Also, R is not symmetric, as (1, 3) ∈ R, but (3, 1) ∉ R [3(3) – 1 ≠ 0].
Also, R is not transitive, as (1, 3), (3, 9) ∈ R, but (1, 9) ∉ R [3(1) – 9 ≠ 0].
Hence, R is neither reflexive, nor symmetric, nor transitive.
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