Consider the division of set A ={1,2,3,4,5,6,7,8} by subsets {1,6} , {2,7},{3,8},{4},{5} define a relation in A by R ={(a,b)} - Maths - Relations and Functions

Question

​Consider the division of set A ={1,2,3,4,5,6,7,8} by subsets
{1,6} , {2,7},{3,8},{4},{5} define a relation in A by R ={(a,b)} a
and b lie in the same subset of the division of A} show that R is
an equivalence relation

Kmebrahim · Answer

R ={(a,b)} a and b lie in the same subset of the division of A} The
elements of R are (1,6), (1,1),(6,1),(6,6),(2,7),
(2,2),(7,2),(7,7),(3,8), (3,3),(8,3),(8,8),(4,4),(5,5) Now for any
a, we have (a,a) element of R R is reflexive Also, for any element
(a,b) in R (b,a) is also in R So, R is symmetric Consider, two
elements (a,b) and (b,c) in R We can see that (a,c) is in R Thus R
is transitive Hence R is an equivalence relation

​Consider the division of set A ={1,2,3,4,5,6,7,8} by subsets {1,6} , {2,7},{3,8},{4},{5}.define a relation in A by R ={(a,b)} a and b lie in the same subset of the division of A} .show that R is an equivalence relation

Consider the division of set A ={1,2,3,4,5,6,7,8} by subsets {1,6} , {2,7},{3,8},{4},{5}.define a relation in A by R ={(a,b)} a and b lie in the same subset of the division of A} .show that R is an equivalence relation