Double Eulerian Tour

Use words to describe the solution process. No programming. 4. Suppose G is a graph. We define a double Eulerian tour as a walk that crosses each edge of G twice in different directions and that starts and ends at the same vertex. Show that every connected graph has a double Eulerian tour.

Relations & Functions / Induction Proof (Discrete Mathematics)

The following commonly recognised family relationships may also be derived. For each of the following derived relationships, construct a predicate corresponding to its defining relational expression: (See attachment for full question)

less composition description

Given the relation "less" over the natural numbers N, describe the compositions as a set of the form {(x,y) | property}. less º less º less

Give an example of a binary relation R such that R is irreflexive but R^2 (R squared) is not irreflexive, and give an example of a binary relation R such that R is antisymmetric but R^2 is not antisymmetric.

For each of the following properties, find a binary relation R such that R has that property but R^2 (R squared) does not: (a) irreflexive (b) antisymmetric

Use induction to prove finite set with n elements has 2^n subsets.

Use induction to prove that a finite set with n elements has 2^n subsets.