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Let A = {1, 2, 3, 4, 5} and let R = {(1,2), (2,1), (4,5), (5,4), (1,1), (2,2), (3,3), (4,4), (5,5)} be an equivalence relation on A. Determine the equivalence classes [1], [2] and [4].

1. [1] = [2] = {1,2}, [4] = {4,5}
2. [1] = {1}, [2] = {2}, [4] = {4}
3. [1] = [2] = [4] = {1,2,4,5}
4. [1] = {1,2}, [2] = {2,3}, [4] = {4,5}

Correct answer: [1] = [2] = {1,2}, [4] = {4,5}

Solution

Since 1R2 and 2R1, [1] = [2] = {1,2}; since 4R5 and 5R4, [4] = {4,5} (and [3] = {3}).

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