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.
тЗТ (1, 1), (2, 2), (3, 3) тИИ R
And (1, 1), (2, 1) тИИ R тЗТ (1, 1) тИИ R
However, (2, 1) тИИ R, but (1, 2) тИЙ 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.
тЗТ (1, 1), (2, 2), (3, 3) тИИ R
And (1, 1), (2, 1) тИИ R тЗТ (1, 1) тИИ R
However, (2, 1) тИИ R, but (1, 2) тИЙ 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.