4. a) The 16 relations on the set {0, 1} are listed below.
R1 = Ø
R2 = { (0, 0) }
R3 = { (0, 1) }
R4 = { (1, 0) }
R5 = { (1, 1) }
R6 = { (0, 0), (0, 1) }
R7 = { (0, 0), (1, 0) }
R8 = { (0, 0), (1, 1) }
R9 = { (0, 1), (1, 0) }
R10 = { (0, 1), (1, 1) }
R11 = { (1, 0), (1, 1) }
R12 = { (0, 0), (0, 1), (1, 0) }
R13 = { (0, 0), (0, 1), (1, 1) }
R14 = { (0, 0), (1, 0), (1, 1) }
R15 = { (0, 1), (1, 0), (1, 1) }
R16 = { (0, 0), (0, 1), (1, 0), (1, 1) }
b) Now determine which of these relations are partial order relations, that is, which of these relations are reflexive, antisymmetric and transitive.