Question

5. Show that the relation Rin the set Z of integers, given by
R = [(a,b): 3 divides a - b) is an equivalence relation. Hence fin
equivalence classes of 0, 1 and 2.
I​

Answer 1

Step-by-step explanation:

hey mate here is your answer :

R== (a,b) : 2 divides (a-b)

= (a,b) : 2 divides (a-b)⇒(a−b) is a multiple of 2.

= (a,b) : 2 divides (a-b)⇒(a−b) is a multiple of 2.To find equivalence class 0, put b=0

= (a,b) : 2 divides (a-b)⇒(a−b) is a multiple of 2.To find equivalence class 0, put b=0So, (a−0) is a multiple of 2

= (a,b) : 2 divides (a-b)⇒(a−b) is a multiple of 2.To find equivalence class 0, put b=0So, (a−0) is a multiple of 2⇒ a is a multiple of 2

= (a,b) : 2 divides (a-b)⇒(a−b) is a multiple of 2.To find equivalence class 0, put b=0So, (a−0) is a multiple of 2⇒ a is a multiple of 2So, In set z of integers, all the multiple

= (a,b) : 2 divides (a-b)⇒(a−b) is a multiple of 2.To find equivalence class 0, put b=0So, (a−0) is a multiple of 2⇒ a is a multiple of 2So, In set z of integers, all the multipleof 2 will come in equivalence

= (a,b) : 2 divides (a-b)⇒(a−b) is a multiple of 2.To find equivalence class 0, put b=0So, (a−0) is a multiple of 2⇒ a is a multiple of 2So, In set z of integers, all the multipleof 2 will come in equivalenceclass {0}

= (a,b) : 2 divides (a-b)⇒(a−b) is a multiple of 2.To find equivalence class 0, put b=0So, (a−0) is a multiple of 2⇒ a is a multiple of 2So, In set z of integers, all the multipleof 2 will come in equivalenceclass {0}Hence, equivalence class {0}={2x}

= (a,b) : 2 divides (a-b)⇒(a−b) is a multiple of 2.To find equivalence class 0, put b=0So, (a−0) is a multiple of 2⇒ a is a multiple of 2So, In set z of integers, all the multipleof 2 will come in equivalenceclass {0}Hence, equivalence class {0}={2x}where x = integer (z)

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