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Answer with Step-by-step explanation:
We are given that an equivalence relation P on Z as
Let
if and only if
such that x-y=2k.
We have to show that how the reflexive property and symmetric property of an equivalence relations hold for P on Z.
We know that reflexive property
a is related to a by given relations.
If xPax then we get
Where k=0 and 0 belongs to integers.
Hence, the relation satisfied reflexive property.
Symmetric property :If a is related to b then b is related to b.
If x and y is related by the relation
where k is any integer
k belongs to integers.
Hence, relation satisfied symmetric property.