Translate each of the following sentences into symbolic logic, then find their negation.(a) There exists a non-zero real number a such that a+ x = x, for every real number x.(b) Every non-constant polynomial p(x) is such that its derivative is not zero.(c) For every positive number M, there exists a positive number N such that f(x) > M whenever x > N.(d) Everyone likes someone, but no one likes everyone. (e) Everyone who is majoring in math has a friend who needs help with his/her homework.

Name: Translate each of the following sentences into symbolic logic, then fi
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Description: Translate each of the following sentences into symbolic logic, then find their negation.(a) There exists a non-zero real number a such that a+ x = x, for every real number x.(b) Every non-constant polynomial p(x) is such that its derivative is not ze

Answered: Translate each of the following…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Translate each of the following sentences into symbolic logic, then find their negation.

(a) There exists a non-zero real number a such that a+ x = x, for every real number x.

(b) Every non-constant polynomial p(x) is such that its derivative is not zero.

(d) Everyone likes someone, but no one likes everyone.

(e) Everyone who is majoring in math has a friend who needs help with his/her homework.

Expert Solution

Step 1: Step 1

We have to translate each of the sentences into symbolic logic. And, then we will find its negation.

(a) There exists a non-zero real number a such that $a + x = x$ , for every real number x.

In symbolic logic, $there exists a element of straight real numbers backslash open curly brackets 0 close curly brackets space for all x element of straight real numbers open parentheses a plus x equals x close parentheses$ .

It's negation is $for all a element of straight real numbers backslash open curly brackets 0 close curly brackets space there exists x element of straight real numbers open parentheses a plus x not equal to x close parentheses$ .

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