logical equivalence

Dear student, solve 10 problems based on logical equivalence .

Assignment II

1.. Find the number of integers between 1 and 250 both inclusive that are divisible by any of the integers 2,3,5,7. 2.Prove that an undirected graph has an even number of vertices of odd degree. 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.Draw a graph that is both Eulerian and Hamiltonian. 5.Prove that a connected graph G is Eulerian if and only if all the vertices are of even degree.