Question: Question 2 (a) (b) (C) Let U denote the universal set with n elements, where n e N . Let A Q U be a

Question 2 (a) (b) (C) Let U denote the universal set with n elements, where n e N . Let A Q U be a set with 2241 elements. Determine all the possible value(s) of n such that A x A = Z x E. (6 marks) Prove by mathematical induction that n(n2 l) is divisible by 24, for any positive odd integer n, . (10 marks) A connected planar graph G with 12 vertices has 10 regions. Suppose that the degrees of 10 of the vertices are 5, 4, 4, 3, 3, 3, 3, 3, 2, 2 and the two remaining vertices have the same degree k. Find all the possible value(s) of k. (4 marks)

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