Consider the following statement. If r is any rational number and s is any irrational number, then is irrational. (a) Which of the following is a negation for the statement? O There is a rational number r and an irrational number s such that is rational. O If r is any rational number and s is any irrational number, then is rational. S r O If r is any irrational number and s is any rational number, then is irrational. O There is a rational number r and an irrational number s such that - is irrational. (b) What are some values of r and s for which the give statement is false (that is, for which its negation is true)? (r, s) = |

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Consider the following statement.
If r is any rational number and s is any irrational number, then
is irrational.
(a) Which of the following is a negation for the statement?
O There is a rational number r and an irrational number s such that
is rational.
O If r is any rational number and s is any irrational number, then
is rational.
r
O If r is any irrational number and s is any rational number, then
is irrational.
O There is a rational number r and an irrational number s such that is irrational.
(b) What are some values of r and s for which the given stateme
is false (that is, for which its negation is true)?
(r. 9) - (L
Transcribed Image Text:Consider the following statement. If r is any rational number and s is any irrational number, then is irrational. (a) Which of the following is a negation for the statement? O There is a rational number r and an irrational number s such that is rational. O If r is any rational number and s is any irrational number, then is rational. r O If r is any irrational number and s is any rational number, then is irrational. O There is a rational number r and an irrational number s such that is irrational. (b) What are some values of r and s for which the given stateme is false (that is, for which its negation is true)? (r. 9) - (L
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