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Let R be an equivalence relation defined in the set A = \{1, 2, 3, 4, 5, 6, 7, 8, 9\} by R=( (x, y) : x,ye A, x and y are either both odd or both even)Write all the equivalence classes of set A.
Asked by rginish12 | 04 Oct, 2023, 11:14: AM
The reation R is given by:
R = {(1, 1), (1, 3), (1, 5), (1, 7), (1, 9), (2, 2), (2, 4), (2, 6), (2, 8), (3, 1), (3, 3), .... (9, 7), (9, 9)}
n(R) = 41
Equivalence class of set A is any subset of A which includes all the elements that are related to each other.
If we take a set which contains only odd numbers from set A, we have {1, 3, 5, 7, 9}
If we take a set which contains only odd numbers from set A, we have {2, 4, 6, 8}
These two sets have elements which are related to each other.
Hence, become the equivalence classes.
Answered by Renu Varma | 05 Oct, 2023, 10:42: AM

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