On the set S of all real numbers, define a relation R = {(a, b): a ≤ b}.
Show that R is (i) reflexive, (ii) transitive (iii) not symmetric.
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On the set S of all real numbers, define a relation R = {(a, b): a ≤ b}.
Show that R is (i) reflexive, (ii) transitive (iii) not symmetric.
On the set S of all real numbers, define a relation R = {(a, b): a ≤ b}.
Show that R is (i) reflexive, (ii) transitive (iii) not symmetric.
(i) Reflexivity
Consider a as an arbitrary element on the set S
So we get a ≤ a where (a, a) ∈ R
Hence, R is reflective.
(ii) Transitivity
Consider a, b and c ∈ S where (a, b) and (b, c) ∈ S
We get
(a, b) ∈ R => a ≤ b and (b, c) ∈ R => b ≤ c
Based on the above equation we get
(a, c) ∈ R => a ≤ c
Hence, R is transitive.
(iii) Non symmetry
We know that
(5, 6) ∈ R => 5 ≤ 6
In the same way
(6, 5) ∈ R => 6 ≰ 5
Hence, R is non symmetric.