Define the following relations on A$=\{0,2,7,9\}.$ Answer each of the following questions by listing the index

of the relation. For example, for Part $1$ R$\_(1)$ and R$\_(2)$ are reflexive, simply enter $1,2$ as the answer.

R$\_(0)=\{(7,2),(0,9),(0,7),(0,2),(0,0),(7,9)\}$

R$\_(1)=\{(0,0),(7,7),(2,2),(9,9)\}$

R$\_(2)=\{(9,9),(7,2),(0,0),(2,2),(7,7),(2,7)\}$

R$\_(3)=\{(2,0),(0,0),(7,7),(9,7),(9,9),(9,2)\}$

R$\_(4)=\{(2,9),(7,9),(0,0),(9,7),(2,0),(9,2),(0,2)\}$

Which relations are reflexive?

Which relations are symmetric?

Which relations are anti$-$symmetric?

Which relations are transitive?