discrete f3

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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.

Composition Description of the Relation 'Less'

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

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.