On an MAT102 test Catherine presented the following argument: "To prove that q: ZxZZ, q(x, y) = = x +y is surjective, we first choose any m € Z. Then we set x = 1 and y = m - 1. Since q (x, y) = x+y=1+(m-1) = m, this implies that q is a surjective function." What can be concluded about this proof? [Select]
On an MAT102 test Catherine presented the following argument: "To prove that q: ZxZZ, q(x, y) = = x +y is surjective, we first choose any m € Z. Then we set x = 1 and y = m - 1. Since q (x, y) = x+y=1+(m-1) = m, this implies that q is a surjective function." What can be concluded about this proof? [Select]
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.4: Ordered Integral Domains
Problem 8E: If x and y are elements of an ordered integral domain D, prove the following inequalities. a....
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Please find attached problem. The drop-down menu says (1) The proof is correct. (2) The proof is not valid since values for x and y are chosen incorrectly. (3) The proof is incorrect since we cannot specify the values of the variables without loosing generality of the proof. Please chose one of those options. Thank you
![On an MAT102 test Catherine presented the following argument:
"To prove that q: Z× Z → Z, q(x, y) = x +y is surjective, we first choose any m € Z.
Then we set x = 1 and y = m - 1.
Since q (x, y) = x+y=1+(m− 1) = m, this implies that q is a surjective function."
What can be concluded about this proof? [Select]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F658d0877-d30e-470e-a192-6c902c3b5487%2Fca9d25c5-924e-4384-a71b-d06ee678c893%2Frmo4ejs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:On an MAT102 test Catherine presented the following argument:
"To prove that q: Z× Z → Z, q(x, y) = x +y is surjective, we first choose any m € Z.
Then we set x = 1 and y = m - 1.
Since q (x, y) = x+y=1+(m− 1) = m, this implies that q is a surjective function."
What can be concluded about this proof? [Select]
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