I am having trouble finding out how to code this. I understand what each one is and know how to tell by looking but cannot figure out how to create functions to check whether it is either reflexive, symmetric, anti-symmetric, and/or transitive (it can be more than one). Here is the exact problem. Given a set of binary relations, determine whether the set is reflexive, symmetric, anti symmetric and/or transitive. Here are the sets:

0 1 2 3

0 0

1 1

2 2

3 3

x y z

x y

y z

y y

z z

x y z

x x

y z

x y

z y

x z

y y

z x

y x

z z

1 2 3 4 5 6 7 8

1 4

1 7

2 5

2 8

3 6

4 7

5 8

6 6

1 1

2 2