Solution Found!
The quantifier n denotes "there exists exactly n,” so that
Chapter 1, Problem 26E(choose chapter or problem)
The quantifier \(\exists_{n}\) denotes "there exists exactly \(n\)," so that \(\exists_{n} x P(x)\) means there exist exactly \(n\) values in the domain such that \(P(x)\) is true. Determine the true value of these statements where the domain consists of all real numbers.
a) \(\exists_{0} x\left(x^{2}=-1\right)\)
b) \(\exists_{1} x(|x|=0)\)
c) \(\exists_{2} x\left(x^{2}=2\right)\)
d) \(\exists_{3} x(x=|x|)\)
Equation Transcription:
Text Transcription:
Exists n
n
Exists_n x P(x)
P(x)
exists_0x (x^2 = -1)
exists_1x (|x| = 0)
Exists_2 x (x^2 = 2)
Exists_3 x (x =|x|)
Questions & Answers
QUESTION:
The quantifier \(\exists_{n}\) denotes "there exists exactly \(n\)," so that \(\exists_{n} x P(x)\) means there exist exactly \(n\) values in the domain such that \(P(x)\) is true. Determine the true value of these statements where the domain consists of all real numbers.
a) \(\exists_{0} x\left(x^{2}=-1\right)\)
b) \(\exists_{1} x(|x|=0)\)
c) \(\exists_{2} x\left(x^{2}=2\right)\)
d) \(\exists_{3} x(x=|x|)\)
Equation Transcription:
Text Transcription:
Exists n
n
Exists_n x P(x)
P(x)
exists_0x (x^2 = -1)
exists_1x (|x| = 0)
Exists_2 x (x^2 = 2)
Exists_3 x (x =|x|)
ANSWER:Solution :
Step 1:
In this problem, we need to determine the true value of these given statements.
Where we are given means there exists exactly n values in the domain such that P(x) is true and the domain consists of all real numbers.
(a): 0x (x2 = -1).
According to the given condition 0x (x2 = -1) means there exists exactly zero(0) value in the domain.