Page 16 - Discrete Structure II

5. R4 = { (5, 5) , (8, 8) , (9, 9)}

Answer

Example I

Let A = {2, 5, 8, 9 }. Which of the following relation on A is symmetric

1. R1 = { (2, 2) , (3, 4), ( 8 , 9 ) , (5, 2) , (5, 5)}

It is not symmetric, because (3,4) ∈ R1 , but (4,3) ∉ R1
2. R2 = { (2, 2) , (3, 4), ( 8 , 9 ) , (4, 3) , (5, 5), (8, 8) , (9, 8)}

It is symmetric

3. R3 = { (2, 5) , (3, 4), ( 8 , 9 ) , (4, 3) , (5, 5), (5, 2) , (8, 8) , (9, 8)}

It is symmetric

4. R4 = { (2, 5) , (5, 2) , (8, 8) , (9, 8)}
5. It is not symmetric, because (9,8) ∈ R1 , but (8,9) ∉ R1

6. R4 = { (5, 5) , (8, 8) , (9, 9)}

It is symmetric.

Exercise

Which of the following relations is reflexive, symmetric?

R1 is not symmetric, for example (5, 8) is an element of R1, but (8, 5) is not an element of R1 ,
because 8 is not less than 5