Question

In the set z of integers, define mrn if m-n is a multiple of 12.prove that R is an equivalence relation: hi bharath how are you? nayabagam iruka​ naanthan sofi

Answer 1

Step-by-step explanation:

mRn if m – n is divisible by 7 (a) mRm = m – m = 0 0 is divisible by 7 ∴ It is reflexive (b) mRn = {m – n) is divisible by 7 nRm = (n – m) = – {m – n) is also divisible by 7 It is symmetric (c) mRn ⇒ (m - n) is divisible by 7 It is transitive mRn if m – n is divisible by 7

it's isha

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Answer 2

Step-by-step explanation:

Relation mRn defined on set of integers Z

m-n is a multiple of 12.

To prove:

The relation R is an equivalence relation.

Solution:

First of all, let us have a look at the definition of equivalence relation.

A relation R defined on set Z is known as equivalence relation if it is:

1. Reflexive:

if

2. Symmetric

if

3. Transitive:

The given relation is:

1. Reflexive:

0 is a multiple of 12, .

2. Symmetric:

Both are multiple of 12, .

3. Transitive:

.... (1)

.... (2)

Adding (1) and (2):

Hence, . .

Hence proved that the relation R is equivalence relation.

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hru