QuestionQuestion

(1) Write the following sets using the notation {x ∈ -- I --}
c) The circle of radius T, centered at the origin (0,0), in the xy-plane.

3) Prove that A = B, where A = {x ∈ Z | ∃y ∈ Z satisfying x = 6y} and B = {x ∈ Z | ∃u, v ∈ Z satisfying x = 2u, x = 3v}.
You may assume standard facts from high school algebra. The symbol ∃ means "there exists".

4) Give an example of a function between two non-mathematical sets. Give an example of something that is not a function.

5) Construct a function f : R -> Z that is onto.

6) Find the natural domain/target sets of the following function
F(x,y) = (x² - y, sin(xy)), G(x,y) = x² + y²

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Algebra Problems
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