319ISOL - MAT 319 SPRING 2008 MIDTERM I WRITE YOUR NAME...

This preview shows pages 1–4. Sign up to view the full content.

MAT 319 SPRING 2008 MIDTERM I !!! WRITE YOUR NAME, STUDENT ID BELOW !!! NAME : ID : THERE ARE SIX (6) PROBLEMS. THEY HAVE THE INDICATED VALUE. SHOW YOUR WORK!!! DO NOT TEAR-OFF ANY PAGE NO CALCULATORS NO PHONES ON YOUR DESK: ONLY test, pen, pencil eraser. 1 40pts 2 40pts 3 40pts 4 50pts 5 40pts 6 40pts Total 250pts 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2 !!! WRITE YOUR NAME, STUDENT ID AND LECTURE N. BELOW !!! NAME : ID : LECTURE N. 1. Prove that the number 3 12 is irrational. Solution. By contradiction, assume 3 12 = r/s , where r, s are coprime natural numbers. We get 12 s 3 = r 3 . Then 2 divides r, so that r = 2 r 1 . We get 2 2 · 3 s 3 = 2 3 r 3 1 . We get 3 s 3 = 2 r 3 1 , so that 2 divides s. This contradicts r, s coprime.
3 2. In each case provide an example or state that it is not possible to do so and explain why. 2a Give one example of a countable set that is not finite. 2b Give one example of a countable set that is not denumerable. 2c Give one example of an uncountable set. 2d Give one example of an uncountable set that is not infinite.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern