In 19-31, (1) prove that the relation is an equivalence relation, and (2) describe the distinct equivalence classes of each relation.
Define P on the
of order paors of real numbers as follows: For every
The given relation is an equivalence relation and also find the distinct equivalence classes of the given relation.
Define P on the set of ordered pairs of real numbers as follows:
For all ,
To prove: P is an equivalent relation.
Let us assume that
By the definition of P :
However, w = y is equivalent with y = w.
Since is symmetric
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