Question

Let R = {(a, b): a, b e Z and (a - b) is divisible by 5).
Show that R is an equivalence relation on Z.
the set A – 11​

Answer 1

Answer:

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)⇒(a−a) is divisible by 5

Symmetric

(a,b)⇔(b,a)

(a−b) is divisible by 5

(b−a) is divisible by 5

Transitive

(a,b),(b,c)⇔(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

Explanation:

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