Question: Disprove each statement by giving a counterexample. (a) n2 + n + 11 is a prime for all positive integers n. (b) n3 ¥ 2n

Disprove each statement by giving a counterexample.
(a) n2 + n + 11 is a prime for all positive integers n.
(b) n3 ‰¥ 2n for all integers n ‰¥ 2.
(c) If n ‰¥ 2 points are arranged on a circle in such a way that no three of the lines joining them have a common point, show that these lines divide the circle into 2n-1 regions.
[The cases n = 2, 3, and 4 are shown in the diagram.]

n=3

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