Show that the relation `R` in the set `A={x: x in N,x <=10}` given by `R={(a, b):a+ b` is even number] is an equivalence relation. Also find the set of all elements related to `3`

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?

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

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 of all the books in a library of a college,given by R={(x,y):x and y have same number of pages } is an equivalence relation.

Show that the relation R on the set A of all the books in a library of a college given by R={(x,y):x and y have the same number of pages }, is an equivalence relation.

Let n be a positive integer.Prove that the relation R on the set Z of all integers numbers defined by (x,y)in R hArr x-y is divisible by n, is an equivalence relation on Z .

Let R be the relation on set A={x:x in Z, 0 le x le 10} given by R={(a,b):(a-b) "is divisible by " 4} . Show that R is an equivalence relation. Also, write all elements related to 4.