Question -
Answer -
(i) The relation on A having properties of being reflexive, transitive, but not symmetric is
R = {(1, 1), (2, 2), (3, 3), (4, 4), (2, 1)}
Relation R satisfies reflexivity and transitivity.
⇒ (1, 1), (2, 2), (3, 3) ∈ R
And (1, 1), (2, 1) ∈ R ⇒ (1, 1) ∈ R
However, (2, 1) ∈ R, but (1, 2) ∉ R
(ii) The relation on A having properties of being reflexive, transitive, but not symmetric is
R = {(1, 1), (2, 2), (3, 3), (4, 4), (2, 1)}
Relation R satisfies reflexivity and transitivity.
⇒ (1, 1), (2, 2), (3, 3) ∈ R
And (1, 1), (2, 1) ∈ R ⇒ (1, 1) ∈ R
However, (2, 1) ∈ R, but (1, 2) ∉ R
(iii) The relation on A having properties of being symmetric, reflexive and transitive is
R = {(1, 1), (2, 2), (3, 3), (4, 4), (1, 2), (2, 1)}
The relation R is an equivalence relation on A.