Question

prove that the realtion of 'conguruence modulo m' in the set of integer Z is an equvalence relation
plz answer me correctly ​

Answer 1

Answer:

YouR ANSWER

If R be the relation,

xRy⇔x−y is divisible by m.

xRx because x−x is divisible by m. So, R is

reflexive.

xRy⇒x−y is divisible by m.

⇒y−x is divisible by m.

⇒yRx

So, R is symmetric

xRy and yRz

Also, x−y=k

1

m,y−z=k

2

m

∴x−z=(k

1

+k

2

)m.So, R is transitive.

As R is reflexive, symmetric and transtive, so it is an equivalence relation.

Step-by-step explanation:

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Answer 2

Answer:

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