Solution Found!
Rewrite the following statements less formally, without
Chapter 1, Problem 7E(choose chapter or problem)
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 property that \(u+v<u-v\).
b. There is a real number \(x\) such that \(x^{2}<x\).
c. For all positive integers \(n, n^{2} \geq n\).
d. For all real numbers \(a\) and \(b,|a+b| \leq|a|+|b|\).
Questions & Answers
QUESTION:
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 property that \(u+v<u-v\).
b. There is a real number \(x\) such that \(x^{2}<x\).
c. For all positive integers \(n, n^{2} \geq n\).
d. For all real numbers \(a\) and \(b,|a+b| \leq|a|+|b|\).
ANSWER:
Step 1 of 4
Here we have to rewrite the given statements in formal form.
(a) consider the statement
There are real numbers and
with the property that
So we can write the statement in formal form as
“There are real numbers and
whose sum is less than their difference.”
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