Give the order and the degree of the recurrence
a2 n+2 = a2n +2an+4
Is the recurrence homogeneous?
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Let A be an 88 Boolean matrix (i.e. every entry is 0 or 1). If the sum of the entries in A is 51, prove that there is a row i and a column j in A such that the entries in row i and in column j add up to more than 13. Further, show that there are at least 4 such pairs of rows and columns.
Is the graph in Fig. 1 Eulerian? Is it Hamiltonian? Justify your answers.
Make a table of the values of the Boolean function
f (x1;x2;x3) = x2(x1
x3)
Write the function in DNF using the table.
Find the generating function of the recurrence
an = 4an-1-4an-2+1
with initial conditions a0 = 1, a1 = 1.
Is Petersen graph bipartite? Give reasons for your answer.
Write (x z)
(y
z') in CNF and DNF.
Which of the following statements are true and which are false? Give reasons for your answer.
i) ( ~p v q) and (p q) are logically equivalent.
ii) (m+n)! > m!+n! for m, n any positive integers.
iii) The number of distributions of m indistinguishable objects into n distinguishable containers is the same as the number of non-negative integral solutions of the equation x1+x2+....+xn = m.
iv) Sn, the number of subsets of a set with n elements, satisfies a second order linear homogeneous recurrence equation with constant coefficients.
v) K3,4 is Hamiltonian.