Question

A relation R on (0, 1, 2) is given by R = {(0,0), (1, 1), (0, 1), (2, 2), (1, 2)). Then the relation R is

• A. reflexive
• B. symmetric
• C. transitive
• D. symmetric and transitive
• E. equivalence

Answer 1

The Correct Option is A

• Reflexive: A relation R is reflexive if for every element a in the set, (a, a) is in R. Here, we have (0, 0), (1, 1), and (2, 2) in R, which means the relation is reflexive.
• Symmetric: A relation R is symmetric if for every (a, b) in R, (b, a) is also in R. In this case, (0, 1) is in R, but (1, 0) is not. Therefore, the relation is not symmetric.
• Transitive: A relation R is transitive if whenever (a, b) and (b, c) are in R, (a, c) is also in R. We have (0, 1) and (1, 2) in R, but (0, 2) is missing, so the relation is not transitive.
• Equivalence: A relation is an equivalence if it is reflexive, symmetric, and transitive. Since R is not symmetric or transitive, it is not an equivalence.

Conclusion:

The relation R is reflexive.