* Total Preorder: x ≲ b or b ≲ a (totality).if a ≲ b and b ≲ c then a ≲ c (transitivity). x ≲ b (reflexivity; implied by transitivity and totality)
Correction: * Total Preorder: a ≲ b or b ≲ a (totality). if a ≲ b and b ≲ c then a ≲ c (transitivity). a ≲ a (reflexivity; implied by transitivity and totality)