In 19-31, (1) prove that the relation is an equivalence relation, and (2) describe the distinct equivalence dasses of each relation.
Define Q on the set
as follows: For every
The given relation is an equivalence relation and also find the distinct equivalence classes of given relation.
Define Q on the set as follows:
To prove: Q is an equivalence relation.
Let us assume that
By the definition of Q :
However, x = z is equivalent with z = x.
Since is symmetric
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