Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
(a.) Find an example of a formula with at least two quantifiers that is false when we quantify over the natural numbers N, but true when we quantify over the rational numbers Q. (a.) Find an example of a formula with one V- quantifier and one 3-quantifier that is true. But alsc your formula should become false when we replace the V-quantifier with an 3-quantifier and the - quantifier with a V-quantifier. Concretely:

(a.) Find an example of a formula with at least two quantifiers that is false when we quantify over the natural numbers N, but true when we quantify over the rational numbers Q. (a.) Find an example of a formula with one V- quantifier and one 3-quantifier that is true. But alsc your formula should become false when we replace the V-quantifier with an 3-quantifier and the - quantifier with a V-quantifier. Concretely:

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
See similar textbooks
icon
Related questions
Question
Question 4 Find examples of formulas with the following characteristics. Explain why your formula is a correct example. (a.) Find an example of a formula with at least two quantifiers that is false when we quantify over the natural numbers N, but true when we quantify over the rational numbers Q. (a.) Find an example of a formula with one V- quantifier and one 3-quantifier that is true. But also, your formula should become false when we replace the V-quantifier with an 3-quantifier and the 3- quantifier with a V-quantifier. Concretely: Your formula Vx ... 3y ... is true .. but Ex ... Vy ... is false .. (You fill in the .…!) Don't forget to say what set you are quantifying over. (Hint: in the lecture and in the book, we have seen examples of formulas that change meaning when we swap the order of the quantifiers. Some of these may work here to0)
Transcribed Image Text:Question 4 Find examples of formulas with the following characteristics. Explain why your formula is a correct example. (a.) Find an example of a formula with at least two quantifiers that is false when we quantify over the natural numbers N, but true when we quantify over the rational numbers Q. (a.) Find an example of a formula with one V- quantifier and one 3-quantifier that is true. But also, your formula should become false when we replace the V-quantifier with an 3-quantifier and the 3- quantifier with a V-quantifier. Concretely: Your formula Vx ... 3y ... is true .. but Ex ... Vy ... is false .. (You fill in the .…!) Don't forget to say what set you are quantifying over. (Hint: in the lecture and in the book, we have seen examples of formulas that change meaning when we swap the order of the quantifiers. Some of these may work here to0)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS