Consider the following statement. For all real numbers x and y, |x| · |y| = |xy|. Which of the following cases must be considered in order to prove the statement? (Select all that apply.) x is a rational number and y is an integer x and y are both rational numbers x = y x is an integer and y is a rational number x and y are both integers x and y are both negative x is nonnegative and y is negative x and y are both nonnegative x is negative and y is nonnegative Write a proof for the statement using a proof format that includes all of the cases you selected. Submit your proof 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.
Added by Joshua W.
Close
Step 1
In this case, we have |x| = -x and |y| = -y. Since the product of two negative numbers is positive, we have |x||y| = (-x)(-y) = xy. Therefore, |x||y| = xy holds true when both x and y are negative. Show more…
Show all steps
Your feedback will help us improve your experience
Sachchidanand Prasad and 89 other Algebra educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Prove that if $x$ and $y$ are rational numbers such that $x>y,$ then there exists a rational number $z$ such that $x>z>y$. (This means that between any two distinct rational numbers there is another rational number.
Rings, Integral Domains, and Fields
Ordered Integral Domains
Use proof by cases to prove that $|x+y| \leq|x|+|y|$ for all real numbers $x$ and $y$.
Proofs
More Methods of Proof
Show that the sum of two rational numbers is rational.
Preliminaries
Real Numbers, Estimation, and Logic
Recommended Textbooks
Elementary and Intermediate Algebra
Algebra and Trigonometry
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD