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BARSIC [14]
3 years ago
10

Define an equivalence relation P on Z as follows: Let x,y e Z ; xPy if and only if ke Z s.t. x - y = 2k Show how the reflexive p

roperty and symmetric property of equivalence relations hold for P on Z.
Mathematics
1 answer:
defon3 years ago
7 0

Answer with Step-by-step explanation:

We are given that an equivalence relation P on Z as

Let x,y\in Z

xPy if and only if k\in Z 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

x-x=0=2(0)

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

x-y=2k where k is any integer

y-x=-2k=2(-k)

k belongs to integers.

Hence, relation satisfied  symmetric property.

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