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Let R={(a, b):a, b Z and (a-b) is divisible by 5}. Show that R

Question

Let $R = {(a, b) : a, b \in Z$ and $(a - b)$ is divisible by $5}$ .
Show that R is an equivalence relation on Z.

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Evelyn Discussed

Let

R = {(a, b) : a, b \in Z

and

(a - b)

is divisible by

5}

.
Show that R is an equivalence relation on Z.

12 mins ago

Discuss this question LIVE

12 mins ago

Text solutionVerified

Given:

R={(a,b):a,b∈Z and (a−b) is divisible by 5}.

R = (a, b)

(a - b)

is divisible by

5

Reflexive

(a, a) \Rightarrow (a - a)

is divisible by

5

Symmetric

(a, b) \Leftrightarrow (b, a)

(a - b)

is divisible by

5

(b - a)

is divisible by

5

Transitive

(a, b), (b, c) \Leftrightarrow (a, c)

(a - b)

is divisible by

5

(b - c)

is divisible by

5

(a - c)

is divisible by

5

R is an equivalent relation on Z

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Question Text	Let $R = {(a, b) : a, b \in Z$ and $(a - b)$ is divisible by $5}$ . Show that R is an equivalence relation on Z.
Answer Type	Text solution:1
Upvotes	150

Let R={(a,b):a,b∈Z and (a−b) is divisible by 5}.Show that R is an equivalence relation on Z.

Text solutionVerified

Practice questions from similar books

Let $R = {(a, b) : a, b \in Z$ and $(a - b)$ is divisible by $5}$ .
Show that R is an equivalence relation on Z.