Proficiency #6. [Predicate Logic] One of the two following statements is always true, for every possible open statement P(x, y) about elements in a universal set U. Decide which is always true, and give an example (when x and y are real numbers, and P(x, y) is a specific concrete open statement – for example, r + y = 1) where the other is false. a. [(3x E U)(Vy e U)(P(x, y))] → [(Vy e U)(3x E U)(P(x, y))] b. [(Vy E U)(3x E U)(P(x, y))] → [(3x € U)(Vy € U)(P(x, y))]

Proficiency #6. [Predicate Logic] One of the two following statements is always true, for every possible open statement P(x, y) about elements in a universal set U. Decide which is always true, and give an example (when x and y are real numbers, and P(x, y) is a specific concrete open statement – for example, r + y = 1) where the other is false. a. [(3x E U)(Vy e U)(P(x, y))] → [(Vy e U)(3x E U)(P(x, y))] b. [(Vy E U)(3x E U)(P(x, y))] → [(3x € U)(Vy € U)(P(x, y))]

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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Question

Proficiency #6. [Predicate Logic] One of the two following statements is always true, for
every possible open statement P(x,y) about elements in a universal set U. Decide which is
always true, and give an example (when x and y are real numbers, and P(x, y) is a specific
concrete open statement – for example, x + y = 1) where the other is false.
a. [Enυ) (Yy EU) (P(π, ))] - [(YυE UJ (Eπε U) (P(π, ))]
b. [(Yy E U) (Eπε υ) (P (s, y))] -Ξε υ) (y ε U (P(τ, 9))

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