Graph Theory.

Show that it is impossible for an odd number of people in a group to each know exactly 2k+1 other people in the group for any integer k.

Let L be a Lattice. Then for every a and b in L (a) a V b = b if and only if a <, or = b (b) a Λ b = a if and only if a <, or = b (c) a Λ b = a if and only if a V b = b

Order Relations and Structures Properties of Lattices Theorem Let L be a Lattice. Then for every a and b in L (a) a V b = b if and only if a <, or = b (b) a Λ b = a if and only if a <, or = b (c) a Λ b = a if and only if a V b = b

Logical reasoning

Sharky, a leader of the underworld, was killed by one of his own band of four henchmen. Detective Sharp interviewed the men and determined that all were lying except one. He deduced who killed Sharky on the basis of the following statements: a. Socko: Lefty killed Sharky. b. Fats: Muscles didn't kill Sharky c. Lefty: Muscles was shooting craps with Socko when Sharky was knocked off. d. Muscles: Lefty didn't kill Sharky. Who did kill Sharky?

Adjacency Matrix.

Find an adjacency matrix for Kn. (That's K 'sub' n)

Adjacency Matrix.

Find an adjacency matrix for Cn. (That's C 'sub' n)