Question

How many anti-symmetric relations on the set A = {1, 2, 3, 4, 5, 6} contain the ordered pairs (2, 2), (3, 4) and (5, 6)?

Answer 1

Anti-symmetric property says: If R(a,b) and R(b,a), then a = b.

In set A = {1, 2, 3, 4, 5, 6} , all the ordered pairs i.e. (2, 2), (3, 4) and (5, 6) are anti-symmetric because:

1. (2,2) - This is an identity relation on set A, so it is an anti-symmetric relation

2. (3,4) - This is an anti-symmetric relation because its opposite (4,3) is not present

3. (5,6) - This is an anti-symmetric relation because its opposite (6,5) is not present