Msc or PhD in mathematics needed for a Discrete Mathematics task

Task example is shown here on attached file.

Skills required
Logic: truth value tables, derivations, disjunctive and subjunctive normal form
and predicate logic formalism.
l Set theory: duality principle, de Morgan's laws, principle of inclusion and
exclusion.
l Relations and functions: theory of functions, properties of relations,
equivalence relations, order relations, matrix and
graph representation of
relations.
l Induction: the principle of ordering, mathematical induction, recursion.
Generating functions.
Dnr: 2015/20653.1.2
l Logic: truth value tables, derivations, disjunctive and subjunctive normal form.
and predicate logic formalism.
l Set theory: duality principle, de Morgan's laws, principle of inclusion and
exclusion.
l Relations and functions: theory of functions, properties of relations,
equivalence relations, order relations, matrix and
graph representation of
relations.
l Induction: the principle of ordering, mathematical induction, recursion.
l Generating functions.
l Combinatorics.
l Difference equations.
l Graphs: Euler circles, Hamiltonian orbits, plane graphs, colouring of graphs and
chromatic polynomials and something about trees.