For each of these relations on the set $111,222,333,444,$ decide whether it is reflexive,

symmetric, antisymmetric, and$/$or transitive. Justify your answer.

$($a$)\{(222,222),(222,333),(222,444),(333,222),(333,333),(333,444)\}$

$($b$)\{(111,111),(111,222),(222,111),(222,222),(333,333),(444,444)\}$