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Question
determination of whether the following relations are reflexive, symmetric, and transitive:
Relation R in the set N of natural numbers defined as
R = {(x, y): y = x + 5 and x < 4}
Solution
R = {(x, y): y = x + 5 and x < 4} = {(1, 6), (2, 7), (3, 8)}
It is seen that (1, 1) ∉ R.
∴R is not reflexive.
(1, 6) ∈R
But,
(6, 1) ∉ R.
∴R is not symmetric.
Transitive
(1, 6) E Rand (6, 7) ∉ R, and (1, 7) ∉ R
∴ R is transitive.
Hence R is neither reflexive, nor symmetric but transitive.
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