The 1985 2nd edition added:
If someone says “updated PDF,” they almost always mean the 2nd edition. liu elements of discrete mathematics pdf upd
Despite newer books like Rosen’s Discrete Mathematics and Its Applications or Epp’s Discrete Mathematics with Applications, Liu’s book remains popular because: The 1985 2nd edition added:
However, the search for an "updated PDF" arises because the book is out of print in many countries, and used copies sell for $50–$150. Students naturally turn to digital libraries. If someone says “updated PDF,” they almost always
Covering basic definitions (vertices, edges, paths, cycles), connectivity, Eulerian and Hamiltonian paths. Liu also introduces trees, spanning trees, and planar graphs. The exercises include classic problems like the "Seven Bridges of Königsberg."
This is where Liu shines. He covers Cartesian products, equivalence relations (reflexive, symmetric, transitive), partial orders, and Hasse diagrams. Functions are treated as special relations, covering injection, surjection, and bijection.