[4 Points] Let x be a positive real number. Prove that if m is irrational (i., not a rational1 number), then is also irrational. For full credit...
View the step-by-step solution to:

Question  1. [4 Points] Let x be a positive real number. Prove that if m is irrational (i.e., not a rational1
number), then ﬂ is also irrational. For full credit your proof should be simple. 2. [4 Points] Additional Exercise 2.5.1(a). (Proof by cases.) Prove the statement: If a: is an
integer, then 1:2 + 5:1: — 1 is odd. 3. [6 Points] (Proof by cases) A perfect square is an integer n of the form n = m2 for some
integer m. Prove that every odd perfect square is of the form 8]»: + 1 for some integer k. 4. [8 Points] Consider the sets A = {2,6,7}, B = {2,4,9}, 0 = {1,2,4,5,7}. Use the
listing method (including commas and braces) to describe the following sets. (a) AUB
(b) 300
(c) AUBUC
(d) AﬂBﬂC
(e) (AUB)ﬂC
(f) AU(BﬂC)

Why Join Course Hero?

Course Hero has all the homework and study help you need to succeed! We’ve got course-specific notes, study guides, and practice tests along with expert tutors.

-

Educational Resources
• -

Study Documents

Find the best study resources around, tagged to your specific courses. Share your own to gain free Course Hero access.

Browse Documents