Suppose we want to prove: "If n is an even natural number, then for all x € R, x" ≥ 0." Classify each of the following as either a mistake or the beginning of a direct proof, proof by contrapos- itive, or proof by contradiction. Let n be an even natural number. Suppose there exists an x ER such that x" <0. Let n be an odd natural number, and suppose that for all x € R, x ≥ 0. Let n be an even natural number. Suppose that for all x € R, x² <0. Take an arbitrary n E N. Suppose there exists an x € R such that x" <0. Let n be any odd natural number.

Suppose we want to prove: "If n is an even natural number, then for all x € R, x" ≥ 0." Classify each of the following as either a mistake or the beginning of a direct proof, proof by contrapos- itive, or proof by contradiction. Let n be an even natural number. Suppose there exists an x ER such that x" <0. Let n be an odd natural number, and suppose that for all x € R, x ≥ 0. Let n be an even natural number. Suppose that for all x € R, x² <0. Take an arbitrary n E N. Suppose there exists an x € R such that x" <0. Let n be any odd natural number.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.2: Mathematical Induction

Problem 49E: Show that if the statement is assumed to be true for , then it can be proved to be true for . Is...

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