Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Let's now examine the result of combining three elements of the set. How do we find the result of 6 + 8 + 11? We notice that there are two possibilities. First, we can perform 68 (2) and then perform 2 11 (1). Second, we can perform 8 11 (7) and then 6 + 7 (1). In this case we see that (68) 11 = 1 and 6 (8 11) = 1. In other words, (68) + 11 = 6 (811). An operation "o" is associative if (x oy)oz=xo (yoz) for every three elements x, y, and z in set S. In this example we can verify that (x + y) + z = x (y z) for every three elements x, y, and z in set S. In other words, is an associative operation.

Let's now examine the result of combining three elements of the set. How do we find the result of 6 + 8 + 11? We notice that there are two possibilities. First, we can perform 68 (2) and then perform 2 11 (1). Second, we can perform 8 11 (7) and then 6 + 7 (1). In this case we see that (68) 11 = 1 and 6 (8 11) = 1. In other words, (68) + 11 = 6 (811). An operation "o" is associative if (x oy)oz=xo (yoz) for every three elements x, y, and z in set S. In this example we can verify that (x + y) + z = x (y z) for every three elements x, y, and z in set S. In other words, is an associative operation.

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
See similar textbooks
icon
Related questions
Question
Let’s now examine the result of combining three elements of the set. How do we find the result of \(6 \oplus 8 \oplus 11\)? We notice that there are two possibilities. First, we can perform \(6 \oplus 8 (2)\) and then perform \(2 \oplus 11 (1)\). Second, we can perform \(8 \oplus 11 (7)\) and then \(6 \oplus 7 (1)\). In this case we see that \((6 \oplus 8) \oplus 11 = 1\) and \(6 \oplus (8 \oplus 11) = 1\). In other words, \((6 \oplus 8) \oplus 11 = 6 \oplus (8 \oplus 11)\). An operation “o” is associative if \((x \circ y) \circ z = x \circ (y \circ z)\) for every three elements \(x, y,\) and \(z\) in set S. In this example we can verify that \((x \oplus y) \oplus z = x \oplus (y \oplus z)\) for every three elements \(x, y,\) and \(z\) in set S. In other words, \(\oplus\) is an associative operation. **Question:** Is multiplication of integers an associative operation?
Transcribed Image Text:Let’s now examine the result of combining three elements of the set. How do we find the result of \(6 \oplus 8 \oplus 11\)? We notice that there are two possibilities. First, we can perform \(6 \oplus 8 (2)\) and then perform \(2 \oplus 11 (1)\). Second, we can perform \(8 \oplus 11 (7)\) and then \(6 \oplus 7 (1)\). In this case we see that \((6 \oplus 8) \oplus 11 = 1\) and \(6 \oplus (8 \oplus 11) = 1\). In other words, \((6 \oplus 8) \oplus 11 = 6 \oplus (8 \oplus 11)\). An operation “o” is associative if \((x \circ y) \circ z = x \circ (y \circ z)\) for every three elements \(x, y,\) and \(z\) in set S. In this example we can verify that \((x \oplus y) \oplus z = x \oplus (y \oplus z)\) for every three elements \(x, y,\) and \(z\) in set S. In other words, \(\oplus\) is an associative operation. **Question:** Is multiplication of integers an associative operation?
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS