List of binary relations

Binary relation	sym	asym	con	wf	join	meet
Equivalence relation	✓	✗	✗	✗	✗	✗
Preorder (Quasiorder)	✗	✗	✗	✗	✗	✗
Partial order	✗	✓	✗	✗	✗	✗
Total preorder	✗	✗	✓	✗	✗	✗
Total order	✗	✓	✓	✗	✗	✗
Prewellordering	✗	✗	✓	✓	✗	✗
Well-quasi-ordering	✗	✗	✗	✓	✗	✗
Well-ordering	✗	✓	✓	✓	✗	✗
Lattice	✗	✓	✗	✗	✓	✓
Join-semilattice	✗	✓	✗	✗	✓	✗
Meet-semilattice	✗	✓	✗	✗	✗	✓

Legend:
  sym : Symmetric
  asym: Antisymmetric
  con : Connex
  wf  : Well-founded
  join: Has joins
  meet: Has meets