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3. Write the following statements in symbolic language and prove each of them: (a) for all r ER, √5-r and √5 +r cannot both be rational. (1) n. Al CAL C CAL C

3. Write the following statements in symbolic language and prove each of them: (a) for all r ER, √5-r and √5 +r cannot both be rational. (1) n. Al CAL C CAL C

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
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**Problem Statement for Educational Website:** 3. Write the following statements in symbolic language and prove each of them: (a) For all \( r \in \mathbb{R} \), \(\sqrt{5} - r\) and \(\sqrt{5} + r\) cannot both be rational. (b) Every prime number \( p \in \mathbb{P}_{>3} \) is either of the form \( 4n + 1 \) or of the form \( 4n + 3 \) for some \( n \in \mathbb{N} \). (c) If \( x \) is irrational and \( y \) is rational then \( xy \) is irrational.
Transcribed Image Text:**Problem Statement for Educational Website:** 3. Write the following statements in symbolic language and prove each of them: (a) For all \( r \in \mathbb{R} \), \(\sqrt{5} - r\) and \(\sqrt{5} + r\) cannot both be rational. (b) Every prime number \( p \in \mathbb{P}_{>3} \) is either of the form \( 4n + 1 \) or of the form \( 4n + 3 \) for some \( n \in \mathbb{N} \). (c) If \( x \) is irrational and \( y \) is rational then \( xy \) is irrational.
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