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QUESTION 3 Arrange steps in approaching proof of the theorem. If direct proof doesn't lead to any result, try a proof by contraposition or by contradiction. v Expand definitions in the hypotheses. Start to reason using the hypotheses together with axioms and available theorems. v Evaluate whether a direct proof looks promising

QUESTION 3 Arrange steps in approaching proof of the theorem. If direct proof doesn't lead to any result, try a proof by contraposition or by contradiction. v Expand definitions in the hypotheses. Start to reason using the hypotheses together with axioms and available theorems. v Evaluate whether a direct proof looks promising

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.2: Mathematical Induction
Problem 50E: Show that if the statement 1+2+3+...+n=n(n+1)2+2 is assumed to be true for n=k, the same equation...
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QUESTION 3 Arrange steps in approaching proof of the theorem. v If direct proof doesn't lead to any result, try a proof by contraposition or by contradiction. v Expand definitions in the hypotheses. v Start to reason using the hypotheses together with axioms and available theorems. Evaluate whether a direct proof looks promising QUESTION 4 For which of the following statements a direct proof is the most efficient? O The sum of two irrational numbers is irrational. O If n is an integer and 3n+2 is odd, then n is odd. O The product of a non-zero rational number and an irrational number is irrational. O The square of an odd number is odd.
Transcribed Image Text:QUESTION 3 Arrange steps in approaching proof of the theorem. v If direct proof doesn't lead to any result, try a proof by contraposition or by contradiction. v Expand definitions in the hypotheses. v Start to reason using the hypotheses together with axioms and available theorems. Evaluate whether a direct proof looks promising QUESTION 4 For which of the following statements a direct proof is the most efficient? O The sum of two irrational numbers is irrational. O If n is an integer and 3n+2 is odd, then n is odd. O The product of a non-zero rational number and an irrational number is irrational. O The square of an odd number is odd.
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