If the relation R on set A = {1, 2, 3} is defined as R = {(1, 2), (2, 3)}, is R reflexive?
Correct Answer: No, R is not reflexive.
- Step 1: Understand what a reflexive relation is. A relation is reflexive if every element in the set is related to itself.
- Step 2: Identify the elements in set A. The set A is {1, 2, 3}.
- Step 3: List the pairs that would show reflexivity. For set A, the pairs needed for reflexivity are (1, 1), (2, 2), and (3, 3).
- Step 4: Check if these pairs are in the relation R. The relation R is {(1, 2), (2, 3)}.
- Step 5: Look for (1, 1) in R. It is not there.
- Step 6: Look for (2, 2) in R. It is not there.
- Step 7: Look for (3, 3) in R. It is not there.
- Step 8: Since none of the pairs (1, 1), (2, 2), or (3, 3) are in R, conclude that R is not 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.
