1. The binary operation * defined on Z by x * y = 2xy. Show that * is commutative and associative. 2. The binary operation * defined on Z by x * y = 1 + 2x + 2y. Show that * is commutative but not associative. 3. A binary operation, using the symbol @, is defined to be a @ b = 3a + b, where a and b are real numbers. a. What is 8 @ 3? b. Is a @ b commutative? c. Is a @ b associative?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 90E
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(MMW-Aa) Instructions: 1. Show your complete solution to the problem. 2. State clearly your assumptions in your solution. 3. Type only the solutions here, please do not handwritten it. NOTE: ANSWER NO. 3&2 ONLY!
Binary Operations
1. The binary operation * defined on Z by x * y = 2xy. Show that * is commutative and associative.
2. The binary operation * defined on Z by x * y = 1 + 2x + 2y. Show that * is commutative but not
associative.
3. A binary operation, using the symbol @, is defined to be a @ b = 3a + b, where a and b are real
numbers.
a. What is 8 @ 3?
b. Is a @ b commutative?
Is a @ b associative?
C.
Transcribed Image Text:Binary Operations 1. The binary operation * defined on Z by x * y = 2xy. Show that * is commutative and associative. 2. The binary operation * defined on Z by x * y = 1 + 2x + 2y. Show that * is commutative but not associative. 3. A binary operation, using the symbol @, is defined to be a @ b = 3a + b, where a and b are real numbers. a. What is 8 @ 3? b. Is a @ b commutative? Is a @ b associative? C.
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