Home
Class 12
MATHS
Show that each of the relation R in the...

Show that each of the relation R in the set `A={x in Z :0lt=xlt=12}`, given by
(i) `R = {(a , b) : |a b| ` is a multiple of `4}`
(ii) `R = {(a , b) : a = b}`is an equivalence relation. Find the set of all elements related to 1 in each case.

Text Solution

AI Generated Solution

To solve the problem, we need to show that each of the given relations is an equivalence relation and then find the set of all elements related to 1 in each case. ### Step 1: Define the Set A The set \( A \) is defined as: \[ A = \{ x \in \mathbb{Z} : 0 < x < 12 \} \] This means \( A = \{ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 \} \). ...
Promotional Banner

Similar Questions

Explore conceptually related problems

Show that the relation R on the set A={x in Z:0<=x<=12}, given by R={(a,b):|a-b| is a multiple of 4} is an equivalence relation.Find the set of all elements related to 1 i.e.equivalence class [1]

Show that the relation R in the set A={x in N:0<=x<=12 } given by R={ (a,b):|a-b| is a multiple of 4 } is an equivalence relation?

Let the relation R in the set A = {x in Z : 0 le x le 12} , given by R = {(a, b) : |a – b|" is a multiple of "4} . Then [1], the equivalence class containing 1, is:

Show that the relation R on the set A{x in Z;0<=12}, given by R={(a,b):a=b}, is an equivalence relation.Find the set of all elements related to 1.

Show that the relation S in the set A={x in Z:0<=x<=12} given by S={(a,b):a,b epsilon Z,^(-)|a-b| is divisible by 4} is an equivalence relation.Find the set of all elements related to 1.

Show that the relation R in the set A = {1, 2, 3, 4, 5,6,7} given by R = {(a , b) : |a - b| " is even" } , is an equivalence relation.

Let the relation R in the set A = {x in z: 0 le x le 12} given by R= {(a, b) :la - bl is a multiple of 4}. Then [1], the equivalence class containing 1, is:

Show that the relation R on the set A={x in Z;0<=x<=12}, given by R={(a,b):a=b}, is an equivalence relation.Find the set of all elements related to 1.

Show that the relation S on the set : A={x inZ:0lexle12} given by: S = { (a,b):a,binZ,|a-b| is divisible by 3} is an equivalence relation.