(d) If x and y are real numbers and x < y, then x² < y*. (e) If æ and y are positive real numbers and æ < y, then æ² < y? .

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Exercise 2.4.4: Showing a statement is true or false by direct proof or counterexample.
i About
Determine whether the statement is true or false. If the statement is true, give a proof. If the statement is false, give a counterexample.
(a) If x and y are even integers, then x + y is an even integer.
(b) If x + y is an even integer, then x and y are both even integers.
(c) If x2 = y?, then x = y.
(d) If x and y are real numbers and x < y, then x2 < y?.
(e) If x and y are positive real numbers and x < y, then x2 < y?.
Transcribed Image Text:Exercise 2.4.4: Showing a statement is true or false by direct proof or counterexample. i About Determine whether the statement is true or false. If the statement is true, give a proof. If the statement is false, give a counterexample. (a) If x and y are even integers, then x + y is an even integer. (b) If x + y is an even integer, then x and y are both even integers. (c) If x2 = y?, then x = y. (d) If x and y are real numbers and x < y, then x2 < y?. (e) If x and y are positive real numbers and x < y, then x2 < y?.
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