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.

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter9: Sequences, Probability And Counting Theory

Section9.5: Counting Principles

Problem 36SE: The number of 5-element subsets from a set containing n elements is equal to the number of 6-element...

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