A relation R in set A = {1,2,3} is defined as R = { (1,1) , (1,2) , (2,2) , (2,1) , (2,3) } . Which of the following ordered pair shall be added to make it a symmetric relation ?

Options

A. (3,3)
B. (1,3)
C. (3,2)
D. (3,1)

Answer

To determine which ordered pair should be added to the relation R to make it symmetric, we first need to understand the definition of a symmetric relation. A relation R is symmetric if for every pair (a, b) in R, the pair (b, a) is also in R.

Given the relation R = { (1,1), (1,2), (2,2), (2,1), (2,3) }, we will analyze the pairs:

1. **Check existing pairs:**
- (1,1): Its symmetric pair (1,1) is already in R.
- (1,2): Its symmetric pair (2,1) is already in R.
- (2,2): Its symmetric pair (2,2) is already in R.
- (2,1): Its symmetric pair (1,2) is already in R.
- (2,3): Its symmetric pair (3,2) is not in R.

2. **Identify missing pairs for symmetry:**
- The only pair that is missing to satisfy the symmetric condition is (3,2) because (2,3) is in R but (3,2) is not.

3. **Conclusion:**
- To make the relation symmetric, we need to add the pair (3,2).

Thus, the ordered pair that should be added to make the relation symmetric is (3,2).