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Question
Discuss the following relation for reflexivity, symmetricity and transitivity:
On the set of natural numbers the relation R defined by “xRy if x + 2y = 1”
Solution
N = {1, 2, 3, 4, 5, ….}
xRy if x + 2y = 1 R is an empty set
(a) xRx ⇒ x + 2x = 1
⇒ x = 13 ∉ N.
It is not reflexive
xRy = yRx
⇒ x + 2y = 1
It does not imply that y + 2x = 1 as y = 1 − x2
It is not symmetric.
(b) – x = y
⇒ (–1, 1) ∉ N
It is not transitive.
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