Let Z be the set of all integers and `A = {(x, y); x^4-y^4 = 175, x, y in Z},B={(х, у), x>y, x, y in Z}` Then, the number of elements in `AnnB` is

Let R be the relation in the set Z of all integers defined by R= {(x,y):x-y is an integer}. Then R is

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

A relation R is defined on the set of integers Z as follows: R{(x,y):x,y in Z and x-y" is odd"} Then the relation R on Z is -

A relation R on the set of integers Z is defined as follows : (x,y) in R rArr x in Z, |x| lt 4 and y=|x|

Let R be a relation on the set Z of all integers defined by:(x,y) in R implies(x-y) is divisible by n.Prove that (b) (x,y) in R implies(y,x) in R for all x,y,z in Z .

Let R be the relation on the Z of all integers defined by (x ,y) in R x-y is divisible by n . Prove that: (x ,x) in R for all x in Z (x ,y) in R (y ,x) in R for all x ,y in Z (x ,y) in Ra n d(y , z) in R (x ,z) in R for all x ,y ,z in R

The number of elements in the set S = {(x, y, z) : x, y, z in Z, x 2y 3z = 42, x, y, z ge 0} equals __________.

A relation R = {(x, y): x-y is divisible by 4, x, y in Z} is defined on set of integers (Z). Prove that R is an equivalence relation.

Let A={x, y, z} be a given set and a relation R on A ios defined as follows : R={(x,x),(y,y),(z,z),(x,y),(y,z),(z,x)} Then the relation R on A is -