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Let S be the statement: The reciprocal of any irrational number is irrational. ( The reciprocal of a nonzero real number x is (a) Which of the following is the contrapositive of S? O If a real number is not irrational, then its reciprocal is not irrational. O If a real number is irrational, then its reciprocal is irrational. O If the reciprocal of a real number is not irrational, then the number is not irrational. O If the reciprocal of a real number is irrational, then the number is irrational. O If the reciprocal of a real number is not irrational, then the number is irrational. O If the reciprocal of a real number is irrational, then the number is not irrational. Write a proof by contraposition for S as a free response. (Submit a file with a maximum size of 1 MB.) Choose File No file chosen This answer has not been graded yet. (b) Which of the following is a negation for S? O If a real number is not irrational, then its reciprocal is irrational. O If a real number is irrational, then the number is not irrational. O There is an irrational number whose reciprocal is not irrational. O There is a number that is not irrational whose reciprocal is irrational. Write a proof by contradiction for S as a free response. (Submit a file with a maximum size of 1 MB.) Choose File No file chosen

Let S be the statement: The reciprocal of any irrational number is irrational. ( The reciprocal of a nonzero real number x is (a) Which of the following is the contrapositive of S? O If a real number is not irrational, then its reciprocal is not irrational. O If a real number is irrational, then its reciprocal is irrational. O If the reciprocal of a real number is not irrational, then the number is not irrational. O If the reciprocal of a real number is irrational, then the number is irrational. O If the reciprocal of a real number is not irrational, then the number is irrational. O If the reciprocal of a real number is irrational, then the number is not irrational. Write a proof by contraposition for S as a free response. (Submit a file with a maximum size of 1 MB.) Choose File No file chosen This answer has not been graded yet. (b) Which of the following is a negation for S? O If a real number is not irrational, then its reciprocal is irrational. O If a real number is irrational, then the number is not irrational. O There is an irrational number whose reciprocal is not irrational. O There is a number that is not irrational whose reciprocal is irrational. Write a proof by contradiction for S as a free response. (Submit a file with a maximum size of 1 MB.) Choose File No file chosen

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter7: Real And Complex Numbers
Section7.1: The Field Of Real Numbers
Problem 20E: Give counterexamples for the following statements. If and are irrational, then is irrational. If ...
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1 Let S be the statement: The reciprocal of any irrational number is irrational. ( The reciprocal of a nonzero real number x is (a) Which of the following is the contrapositive of S? O If a real number is not irrational, then its reciprocal is not irrational. O If a real number is irrational, then its reciprocal is irrational. O If the reciprocal of a real number is not irrational, then the number is not irrational. O If the reciprocal of a real number is irrational, then the number is irrational. O If the reciprocal of a real number is not irrational, then the number is irrational. If the reciprocal of a real number is irrational, then the number is not irrational. Write a proof by contraposition for S as a free response. (Submit a file with a maximum size of 1 MB.) Choose File No file chosen This answer has not been graded yet. (b) Which of the following is a negation for S? O If a real number is not irrational, then its reciprocal is irrational. O If a real number is irrational, then the number is not irrational. O There is an irrational number whose reciprocal is not irrational. O There is a number that is not irrational whose reciprocal is irrational. Write a proof by contradiction for S as a free response. (Submit a file with a maximum size of 1 MB.) Choose File No file chosen This answer has not been graded yet.
Transcribed Image Text:1 Let S be the statement: The reciprocal of any irrational number is irrational. ( The reciprocal of a nonzero real number x is (a) Which of the following is the contrapositive of S? O If a real number is not irrational, then its reciprocal is not irrational. O If a real number is irrational, then its reciprocal is irrational. O If the reciprocal of a real number is not irrational, then the number is not irrational. O If the reciprocal of a real number is irrational, then the number is irrational. O If the reciprocal of a real number is not irrational, then the number is irrational. If the reciprocal of a real number is irrational, then the number is not irrational. Write a proof by contraposition for S as a free response. (Submit a file with a maximum size of 1 MB.) Choose File No file chosen This answer has not been graded yet. (b) Which of the following is a negation for S? O If a real number is not irrational, then its reciprocal is irrational. O If a real number is irrational, then the number is not irrational. O There is an irrational number whose reciprocal is not irrational. O There is a number that is not irrational whose reciprocal is irrational. Write a proof by contradiction for S as a free response. (Submit a file with a maximum size of 1 MB.) Choose File No file chosen This answer has not been graded yet.
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