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Let S = {1, 2, 3, 4, 5, 6, 7}. The relation R = {(1, 1), (1, 3), (1, 4), (2, 2), (3, 1)

Chapter 5, Problem 2

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QUESTION:

Let S = {1, 2, 3, 4, 5, 6, 7}. The relation R = {(1, 1), (1, 3), (1, 4), (2, 2), (3, 1), (3, 3), (3, 4), (4, 1), (4, 3), (4, 4), (5, 5), (5, 7), (6, 6), (7, 5), (7, 7)} on S is an equivalence relation. Determine the distinct equivalence classes.

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QUESTION:

Let S = {1, 2, 3, 4, 5, 6, 7}. The relation R = {(1, 1), (1, 3), (1, 4), (2, 2), (3, 1), (3, 3), (3, 4), (4, 1), (4, 3), (4, 4), (5, 5), (5, 7), (6, 6), (7, 5), (7, 7)} on S is an equivalence relation. Determine the distinct equivalence classes.

ANSWER:

Step 1 of 3

Equivalence classes for each element  in the set can be defined as follows:

Or we can write that, equivalent class of an element  is the set of elements that related to .

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