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1. Consider a new addition for real numbers, denoted by , and defined as a b = 3a + 3b, where is the regular addition for reals. Is commutative? Is associative? If any of your answers are affirmative, argue why it is true for any a and b, if they are negative, construct a concrete counterexample where the property fails. 2. Same questions for ab = 3a + b.

1. Consider a new addition for real numbers, denoted by , and defined as a b = 3a + 3b, where is the regular addition for reals. Is commutative? Is associative? If any of your answers are affirmative, argue why it is true for any a and b, if they are negative, construct a concrete counterexample where the property fails. 2. Same questions for ab = 3a + b.

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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1. Consider a new addition for real numbers, denoted by , and defined as a b = 3a + 3b, where is the regular addition for reals. Is commutative? Is associative? If any of your answers are affirmative, argue why it is true for any a and b, if they are negative, construct a concrete counterexample where the property fails. 2. Same questions for ab= 3a + b.
Transcribed Image Text:1. Consider a new addition for real numbers, denoted by , and defined as a b = 3a + 3b, where is the regular addition for reals. Is commutative? Is associative? If any of your answers are affirmative, argue why it is true for any a and b, if they are negative, construct a concrete counterexample where the property fails. 2. Same questions for ab= 3a + b.
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