If the relation R on set A = {1, 2, 3} is defined as R = {(1, 1), (2, 2), (3, 3)}, is R reflexive?
Correct Answer: Yes, R is reflexive.
- Step 1: Identify the set A. Here, A = {1, 2, 3}.
- Step 2: Understand what a reflexive relation means. A relation is reflexive if every element in the set is related to itself.
- Step 3: Check the relation R. The relation R is given as R = {(1, 1), (2, 2), (3, 3)}.
- Step 4: Look at each element in set A. The elements are 1, 2, and 3.
- Step 5: Verify if each element is related to itself. We see (1, 1), (2, 2), and (3, 3) in R.
- Step 6: Since all elements (1, 2, and 3) are related to themselves, conclude that R is reflexive.
- Reflexive Relation – A relation R on a set A is reflexive if for every element a in A, the pair (a, a) is in R.
