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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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?
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