Question

State whether the following statements are true.

i) R = {(1, 1), (1,3), (3, 3)} is a relation in A = {1, 2, 3, 4} is reflexive.

ii) The relation R1 = {(1, 2), (3,3), (3, 4)} in A = {1, 2, 3, 4} is symmetric.

iii) The relation R2 = {(1, 1), (2. 3), (3, 2), (2, 2)} in A = {1, 2, 3} is antisymmetric.

iv) The relation R3 = {(2, 2), (1, 1), (3, 2), (2, 3), (3, 3)} in A = {1, 2, 3, 4} is transitive.​

Answer 1

Answer:only (iv) option is true

Step-by-step explanation:for (i) option since (2,2) doesnot belongs to set thus it is not reflexive

For (ii) since (1,2) belongs to R2 but (2,1) doesnot belongs to R2 hence it is not symmetric

For (iii) since (2,3) belongs to R3 and (3,2) belongs to R3 but 2 is not equal to 3 hence it is not antisymmetric