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

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 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.

Show that the relation R on the set A of points in a plane, given by R={(P , Q): Distance of the point P from the origin is same as the distance of the point Q from the origin}, is an equivalence relation. Further show that the set of all points related to a point P!=(0, 0) is the circle passing through P with origin as centre.

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.