Let R be the relation in the set Z of integers given by R = {(a, b) :

1.	Let R be the relation in the set Z of integers given by R = {(a, b) : 2 divides a – b}.Show that the relation R transitive? Write the equivalence class [0].
Answer» Let 2 divides(a - b) and 2 divides (b - c) where a, b, c ∈ z So 2 divides [(a – b) + (b − c)] 2 divides (a – b): Yes relation R is transitive [0] = {0, ± 2, ± 4, ± 6,...}

Let R be the relation in the set Z of integers given by R = {(a, b) : 2 divides a – b}.Show that the relation R transitive? Write the equivalence class [0].

Answer»

Let 2 divides(a - b) and 2 divides (b - c)

where a, b, c ∈ z

So 2 divides [(a – b) + (b − c)]

2 divides (a – b): Yes relation R is transitive

[0] = {0, ± 2, ± 4, ± 6,...}

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Let R be the relation in the set Z of integers given by R = {(a, b) : 2 divides a – b}.Show that the relation R transitive? Write the equivalence class [0].

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