Logical equivalence

Dear students, solve 10 problems based on equivalence

Assignment II

1.Prove that a connected graph G is Eulerian if and only if all the vertices are of even degree. 2.Draw a graph that is both Eulerian and Hamiltonian. 3.Give an example of a graph which is 1)Eulerian but not Hamiltonian 2) Hamiltonian but not Eulerian 3) Hamiltonian and Eulerian 4)Neither Hamiltonian or Eulerian 4.Find the number of integers between 1 and 250 both inclusive that are divisible by any of the integers 2,3,5,7. 5.Prove that an undirected graph has an even number of vertices of odd degre