An equivalence relation is a binary relation that is reflexive, symmetric, and transitive. To determine if a relation is an equivalence relation, one must check that for any elements a and b, a is related to a (reflexive), if a is related to b then b is related to a (symmetric), and if a is related to b and b is related to c, then a is related to c (transitive). To find the equivalence classes, one identifies all element pairs in the relation and finds those that contain a specific element like 0.

1. Equivalence Relations
Steve Paks

2. Equivalence Relations
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Definition
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it is symmetric, reflexive, and transitive
reflexive
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symmetric
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x = y implies y = x
transitive
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x=x
x = y and y = z implies that x = z
Determining Equivalence Relations
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reading in and storing equivalence pairs <i, j>
finding all pairs of the form<0, j>
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0 and j are in the same equivalence class