Question

Let R be a relation defined on the set of all integers defined by R={(a,b) : 2 divides a-b}
a) show that R is an equivalence relation?
b) Find [o] & [1].
c)Show that &[1] form a partition of Z.​

Answer 1

Step-by-step explanation:

Set A={0,1,2,3,4,5}  

R be the equivalence relation on A.

Set R={(a,b)2divides(a−b)}

We have to find equivalnce class [0]

To find equivalence class {0},put b=0

⇒a−0 is multiple of 2 .  

⇒ a is multiple of 2.  

Multiples of 2 in given set are 0,2 and 4 .  

Hence equivalence class {0}={0,2,4}

I hope it helps you

Answer 2

Set A={0,1,2,3,4,5}

R be the equivalence relation on A.

Set R={(a,b)2divides(a−b)}

We have to find equivalnce class [0]

To find equivalence class {0},put b=0

⇒a−0 is multiple of 2 .

⇒ a is multiple of 2.

Multiples of 2 in given set are 0,2 and 4 .

Hence equivalence class {0}={0,2,4}

I hope it helps you

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