Check wether the graph in Fig. 1 is Eulerian or not. Is it regular? Justify your answer.

Prove that the graph given below is non-Hamiltonian.

Obtain the CNF of the Boolean expression 

Using the principle of mathematical induction show that the sum of the cubes of three successive positive integers is divisible by 9.

Using the method of generating functions, solve the recurrence relation 

Look at the following pattern:

(i) How many ′ + ′ signs should be there in the box?

(ii) What are the smallest and largest integers in the box?

For any propositions