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Which of the following statements are true and which are false? Give reasons for your answer. i) (∼ p∨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.
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