Question
Asked Jan 8, 2020
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Rewrite the following statements less formally,
without using variables. Determine, as best as you
can, whether the statements are true or false.
a. There are real numbers u and v with the prop-
erty that u + v < u v.
b. There is a real number x such that x< x.
c. For every positive integer n, n² >n.
d. For all real numbers a and b, |a+b|< ]a|+[b|.
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Rewrite the following statements less formally, without using variables. Determine, as best as you can, whether the statements are true or false. a. There are real numbers u and v with the prop- erty that u + v < u v. b. There is a real number x such that x< x. c. For every positive integer n, n² >n. d. For all real numbers a and b, |a+b|< ]a|+[b|.

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Expert Answer

Step 1

(a) The given statement is true.

For example, take

Advanced Math homework question answer, step 1, image 1
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Step 2

Hence, there exists real numbers u and v such that their sum is less than their difference.

Less formally, we can write there exists two real numbers such that their sum is less than the difference between them.

(b) The given statement is true.

Advanced Math homework question answer, step 2, image 1
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Step 3

Specifically, this is true for any x lying between -1 and 1.

Less formally, we can write there exists a real number whose square is l...

Advanced Math homework question answer, step 3, image 1
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