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]

Question

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]

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].

Monjur Alahi

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2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Let 2 divides `(a-b)` and 2 divides `(b-c)` : where `a,b,c, in Z`
So 2 divides `[(a-b)+(b-c)]`
2divides `(a-c)` : Yes relation R is transitive
`[0]={0,+-2,+-4,+-6,....}`

9 views Answered 2023-02-05 15:29