## Problem-44

**Problem-44**

For each of these relations on the set {1,2,3,4}, decide whether it is reflexive, whether it is symmetric, whether it is antisymmetric, and whether it is transitive.

**a)** {(2,2),(2,3),(2,4),(3,2),(3,3),(3,4)}

**b)** {(1,1),(1,2),(2,1),(2,2),(3,3),(4,4)}

**c)** {(1,4),(4,1)}

**d)** {(1,2),(2,3),(3,4)}

**e)** {(1,1),(2,2),(3,3),(4,4)}

**f)** {(1,3),(1,4),(2,3),(2,4),(3,1),(3,4)}

**Solution**

**a)** {(2,2),(2,3),(2,4),(3,2),(3,3),(3,4)}

Transitive

**b)** {(1,1),(1,2),(2,1),(2,2),(3,3),(4,4)}

Transitive

Reflexive

Symmetric

**c)** {(1,4),(4,1)}

Symmetric

**d)** {(1,2),(2,3),(3,4)}

Antisymmetric

**e)** {(1,1),(2,2),(3,3),(4,4)}

Antisymmetric

Reflexive

Symmetric

Transitive

**f)** {(1,3),(1,4),(2,3),(2,4),(3,1),(3,4)}

None of the above properties.