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Relations and Functions
Question
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Determine whether each of the following relations are reflexive, symmetric and transitive :
(ii) Relation R in the set N of natural numbers defined as R = {(x, y) : y = x + 5 and x < 4}

Answer

Relation R is in the set N given by
R = {(x, y) : y = x + 5 and x < 4 }
∴ R = {(1,6), (2, 7). (3, 8)}
(a) R is not reflexive as (x, x) ∉ R (b) R is not symmetric as (x, y) ∈ R ⇏ (v, x) ∈ R (c ) R is not transitive as (x,y) ∈ R, (y, z) ∈ R ⇏ (x, z) ∈ R

Sponsor Area

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