Which of these relations is symmetric?
Which of these relations is symmetric?
Answer: A. R = {(1, 2), (2, 1), (3, 3)}; C. R = {(1, 1), (2, 2), (3, 3)} — Definition: A relation R on a set is symmetric if whenever (a, b) is in R, then (b, a) is also in R. R = {(1, 2), (2, 1), (3, 3)} — symmetric because (1, 2)…
- A.
R = {(1, 2), (2, 1), (3, 3)}
- B.
R = {(1, 2), (2, 3), (3, 1)}
- C.
R = {(1, 1), (2, 2), (3, 3)}
- D.
R = {(1, 2), (2, 1), (3, 2)}
Attempted by 193 students.
Show answer & explanation
Correct answer: A, C
Definition: A relation R on a set is symmetric if whenever (a, b) is in R, then (b, a) is also in R.
R = {(1, 2), (2, 1), (3, 3)} — symmetric because (1, 2) and (2, 1) are both present, and (3, 3) is a self-pair (equal to its reverse).
R = {(1, 2), (2, 3), (3, 1)} — not symmetric because, for example, (1, 2) is present but the reverse (2, 1) is not.
R = {(1, 1), (2, 2), (3, 3)} — symmetric because every pair is a self-pair and therefore equals its reverse.
R = {(1, 2), (2, 1), (3, 2)} — not symmetric because (3, 2) appears but its reverse (2, 3) does not.
Conclusion: The relations that satisfy the symmetry condition among the given choices are R = {(1, 2), (2, 1), (3, 3)} and R = {(1, 1), (2, 2), (3, 3)}.