Order 4 of the following sentences so that they prove the following statement by contradiction: The average of three real numbers is greater than or equal to at least one of the numbers.Proof by contradiction of the statement (in order):Choose from this list of sentencesHence, the assumption that the average of threereal numbers is greater than all of the numbers isfalseAdding up the three inequalities yieldsx+y+z> x+y+zAdding up the three inequalities yieldsx+y+zx, (x+y+z)/3> y, and(x+y+z)/3> <This contradicts the fact thatx+y+z= x+y+zLet x, y and z be real numbers and(x+y+z)/3 < x, (x+y+z)/3 < y, and(x+y+z)/3 Complete the following proof, which proves the statement by contradiction: If a² is even, then a is even.proof.Let a² beBy the definition of odd, there exist integers k such thatIt follows that a² = (2k + 1)² = 4k² + 4k+ 1 = 2(SincePand a beis an integer, and integers are closed undermust be an integer.Thus, by the definition of odd,This contradicts with thatisthis problemis odd. Hence,)+1.andis odd.Hence, the assumption that a² is even and a is odd is false.

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Order 4 of the following sentences so that they prove the following statement by contradiction: The average of three real numbers is greater than or equal to at least one of the numbers. Proof by contradiction of the statement (in order): Choose from this list of sentences Hence, the assumption that the average of three real numbers is greater than all of the numbers is false Adding up the three inequalities yields x+y+z>x+y+z Adding up the three inequalities yields x+y+zx, (x+y+z)/3> y, and (x+y+z)/3> z This contradicts the fact that