A rational number is a real number which can be written as the fraction of two integers. Which of the following shows a formally correct way to define the predicate Rational (x), which tells us that is rational? Rational (x): (Ey € I: 3 € I: x x = ²) Rational (x) → (VxER: Jy I: 32 € I: x = 1) OVER: ByI: 3 €I: Rational (x) + (x = 4) OVER: Rational (x) + (y I: 3 € 1 : x = 4)
A rational number is a real number which can be written as the fraction of two integers. Which of the following shows a formally correct way to define the predicate Rational (x), which tells us that is rational? Rational (x): (Ey € I: 3 € I: x x = ²) Rational (x) → (VxER: Jy I: 32 € I: x = 1) OVER: ByI: 3 €I: Rational (x) + (x = 4) OVER: Rational (x) + (y I: 3 € 1 : x = 4)
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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Transcribed Image Text:Q5
A rational number is a real number which can be written as the fraction of two integers. Which of
the following shows a formally correct way to define the predicate Rational (x), which tells us
that is rational?
O Rational (x): (y € I: 32 € I: x = ½)
Rational (x) → (VxER: Jy I: 32 € I : x = ²)
(x = 4)
OVER: y EI: 32 € I: Rational (a)
OVER: Rational (r) → (y I: 32 € I : x = 4)
Expert Solution
Step 1
The objective is to choose the correct form of .
In words, for any real number , is true if and only if there exist integers and with such that .
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