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Discrete Mathematics With Applicat...
Solutions
Discrete Mathematics With Applicat...
In each of 7-14, relation R is an equivalence relation on the set A. Find the distinct equivalence classes of R.
To find the distinct equivalence classes of R.
Given information:
The relation R is an equivalence relation on the set A. Find the distinct equivalence classes of R.
A = {-4, -3, -2, -1, 0, 1, 2, 3, 4}. R defined on A as follows: For all
Calculation:
Let us first determine which values are in the same equivalence class as − 4. a is in the same equivalence class as − 4, when
Element
− 3 16 − (- 3)2 = 16 − 9 = 7 No
− 2 16 − (- 2)2 = 16 − 4 = 12 No
− 1 16 − (- 1)2 = 16 − 1 = 15 Yes
0 16 − 02 = 16 − 0 = 16 No
1 16 − 12 = 16 − 1 = 15 Yes
2 16 − 22 = 16 − 4 = 12 No
3 16 − 32 = 16 − 9 = 7 No
4 16 − 42 = 16 − 16 = 0 Yes
Thus we then note that − 1, 1 and 4 are in the same equivalence class as − 4, thus the first equivalence class is then
Chapter 8 Solutions
