For each of these relations on the set $\{1,2,3,4\},$ decide whether it is reflexive, whether it is symmetric, and whether it is antisymmetric, and whether it is transitive.
$$
\begin{array}{l}{\text { a) }\{(2,2),(2,3),(2,4),(3,2),(3,3),(3,4)\}} \\ {\text { b) }\{(1,1),(1,2),(2,1),(2,2),(3,3),(3,4)\}} \\ {\text { c) }\{(2,4),(4,2)\}} \\ {\text { d) }\{(1,2),(2,3),(3,4)\}} \\ {\text { e) }\{(1,1),(2,2),(3,3),(4,4)\}} \\ {\text { f) }\{(1,3),(1,4),(2,3),(2,4),(3,1),(3,4)\}}\end{array}
$$
Relations
Relations and Their Properties