3. Recall that a real number is irrational if it is not an element of Q. De- cide whether the following statements are true or false, giving a proof or counterexample as appropriate. (i) For all a, b ER. If a and b are both irrational then a +b is irrational. (ii) For all a, b ER. If a is rational and b is irrational then a+b is irrational. (iii) For all a, b E R. If a and b are both irrational then ab is irrational. (iv) For all a, bER. If a is rational and b is irrational then ab is irrational. Do any of the false statements become true if we insist additionally that a and b are both positive?

3. Recall that a real number is irrational if it is not an element of Q. De- cide whether the following statements are true or false, giving a proof or counterexample as appropriate. (i) For all a, b ER. If a and b are both irrational then a +b is irrational. (ii) For all a, b ER. If a is rational and b is irrational then a+b is irrational. (iii) For all a, b E R. If a and b are both irrational then ab is irrational. (iv) For all a, bER. If a is rational and b is irrational then ab is irrational. Do any of the false statements become true if we insist additionally that a and b are both positive?

Name: 3. Recall that a real number is irrational if it is not an element of
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
Description: 3. Recall that a real number is irrational if it is not an element of Q. De-cide whether the following statements are true or false, giving a proof orcounterexample as appropriate.(i) For all a, b ER. If a and b are both irrational then a +b is irra

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter11: Rational And Irrational Numbers

Section11.1: Properties Of Rational Numbers

Problem 36WE

See similar textbooks