(c) For any positive integer r, a is rational. (d) You can fool some of the people all of the time, and you can fool all of the people some of the time, but you can't fool all of the people all of the time. (Abraham Lincoln). (Use the open sentence F(x, t) to mean you can fool the person a at time t.)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.1: Real Numbers
Problem 36E
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only need in c and d
Translate each of the following sentences into symbolic logic.
(a) For every positive number e, there is a positive number M for which f(x) – 6| < €, whenever
x > M. (This is the definition of lim, f(x) = b.)
(b) There exists a real number a for which a +a = r for every real number r.
(c) For any positive integer r, Va is rational.
(d) You can fool some of the people all of the time, and you can fool all of the people some of
the time, but you can't fool all of the people all of the time. (Abraham Lincoln). (Use the
open sentence F(r, t) to mean you can fool the person a at time t.)
Transcribed Image Text:Translate each of the following sentences into symbolic logic. (a) For every positive number e, there is a positive number M for which f(x) – 6| < €, whenever x > M. (This is the definition of lim, f(x) = b.) (b) There exists a real number a for which a +a = r for every real number r. (c) For any positive integer r, Va is rational. (d) You can fool some of the people all of the time, and you can fool all of the people some of the time, but you can't fool all of the people all of the time. (Abraham Lincoln). (Use the open sentence F(r, t) to mean you can fool the person a at time t.)
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