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Let us read the quantifier ! as "there exists exactly one," so that 3!x, P(x) means that there is a unique r from the domain of x so that P(x) is true. 1. Suppose x is from the domain R of real numbers. Is the following true: 3!x, (x² = 4)? 2. Again, if x is from the domain R, is the following true: 3!x, (x³ = −27)? 3. Still, with x from R, is the following true: 3!x, (x4 = −27)? 4. How do we turn any expression with ! into one using the standard existential (3) and universal quantifiers (V) only?

Let us read the quantifier ! as "there exists exactly one," so that 3!x, P(x) means that there is a unique r from the domain of x so that P(x) is true. 1. Suppose x is from the domain R of real numbers. Is the following true: 3!x, (x² = 4)? 2. Again, if x is from the domain R, is the following true: 3!x, (x³ = −27)? 3. Still, with x from R, is the following true: 3!x, (x4 = −27)? 4. How do we turn any expression with ! into one using the standard existential (3) and universal quantifiers (V) only?

Advanced Engineering Mathematics
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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Let us read the quantifier ! as "there exists exactly one," so that 3!x, P(x) means that there is a unique r from the domain of x so that P(x) is true. 1. Suppose x is from the domain R of real numbers. Is the following true: 3!x, (x² = 4)? 2. Again, if x is from the domain R, is the following true: 3!x, (x³ = −27)? 3. Still, with x from R, is the following true: 3!x, (x4 = −27)? 4. How do we turn any expression with ! into one using the standard existential (3) and universal quantifiers (V) only?
Transcribed Image Text:Let us read the quantifier ! as "there exists exactly one," so that 3!x, P(x) means that there is a unique r from the domain of x so that P(x) is true. 1. Suppose x is from the domain R of real numbers. Is the following true: 3!x, (x² = 4)? 2. Again, if x is from the domain R, is the following true: 3!x, (x³ = −27)? 3. Still, with x from R, is the following true: 3!x, (x4 = −27)? 4. How do we turn any expression with ! into one using the standard existential (3) and universal quantifiers (V) only?
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