## partial ordering

Which of the relations on {0,1,2,3} are partial ordering ? Determine the properties of a partial ordering that the others lack.

(a) {(0,0),(2,2),(3,3)} - it is partial order
(b) { (0,0),(1,1),(2,0),(2,2),(2,3),(3,3)} - it is not partial order since (3,2) and (0,2) missing, not antisymmetric, not transitive
(c) {(0,0),(1,1),(1,2),(2,2),(3,1),(3,3)} - it is partial order
(d) {(0,0),(1,1),(1,2),(1,3),(2,0),(2,2),(2,3),(3,0),( 3,3)} - not antisymmetric, not transitive since (0,3) missing.
(e) {(0,0),(0,1),(0,2),(0,3),(1,0),(1,1),(1,2),(1,3),( 2,0),(2,2),(3,3) } - it is partial order.

Can some one please help me with this and verify this answer ??