Problem 6. Order 7 of the following sentences so that they form a logical proof by contrapositive of the statement: VxEZ, 9x + 15 even ⇒ x is odd • 9x+15=2(9k+7)+1 x is even. • Suppose x is an integer that is not odd. • Then a miracle occurred. • 9x + 15 is even • 9x+15= 9(2k) + 15 = 18k+14+1 • Ek such that x = 2k • 9x + 15 is odd • 9x+15=2j+1 for some integer j • Suppose 9x + 15 is not even.

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