In the set of all natural numbers,let a relation defined by `{(a,b):a,binN,a-b` is divisible by `5}`.Prove that R is an equivalence relation.

Show that the relation 'S' in set A={x inz:0lexle12} given by S={(a,b):a.bin z,|a-b| is divisble by a} is an equivalence relation.

Let T be the set of all triangles in a plane with R a relation in T given by {(T_1,T_2):T_1~=T_2} show that R is an equivalence relation.

Let L be the set of all line in XY place and R be the relation in L defined as R = {(L_1,L_2):L_1 is parallel to L_2 }Show that R is an equivalence relation. Find the set of all line related to the line y=2x+4

Let R be the relation on the set Z of all integers defined by R={(x, y) : x,y in Z,x-y is divisible by n}.Prove that i) (x, x) in R for all x in , Z ii) (x, y) in R implies that (y, x) in R for all x, y in Z iii) (x, y) in R and (y, z) in R implies that (x, z) in R for all x, y, z in Z

Let A={1,2,3,4,6} and R be a relation on A defined by R={(a,b): a, b in A, b is exactly divisible by a} Find the domain and range of R.

If R is a relation on the set N of natural numbers defined by a+3b=12 .Find R.

Let A={1,2,3,4,6} and R be a relation on A defined by R={(a,b): a,b in A, b is exactly divisible by a} Write R in the roster form.

Let A={1,2,3,4,6} .Let R be the relation on A defined by R={(a,b):a,b in A, b is exactly divisible by a} Find the range of R.

Let A={1,2,3,4,6} .Let R be the relation on A defined by R={(a,b):a,b in A, b is exactly divisible by a} Write R in roster form.

Let ast be a binary operation on the set of all real numbers R defined by aastb=a+b+a^2b for a, b belongs to R. Prove that ast is neither commutative nor associative.