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Question
determination of whether the following relations are reflexive, symmetric, and transitive:
Relation R in the set A = {1, 2, 3...13, 14} defined as R = {(x,y):3x - y = 0}
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, 2), (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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