A relation S is defined on the set of real numbers `R R` a follows:
S={(x,y) : s,y `in R R ` and and x= +-y}
Show that S is an equivalence relation on `R R`.

A relation R is defined on the set of integers Z Z as follows R= {(x,y) :x,y inZ Z and (x-y) is even } show that R is an equivalence relation on Z Z .

A relation R_(1) is defined on the set of real number R R as follows : R_(1) ={(x,y) : 1+xy gt 0 , x inR R y in R R } Show that R_(1) is reflexive and symmetric but not transitive on R R .

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 -

Let S be the set of all rest numbers and lets R={(a,b):a,bin S and a=+-b}. Show that R is an equivalence relation on S.

A relation S is defined on the set of real numbers R R a follows : S{(x,y) : x^(2) +y^(2)=1 for all x,y in R R } Check the relation S for (i) reflexivity (ii) symmetry an (iii) transitivity.

If I is the set of real numbers, then prove that the relation R={(x,y) : x,y in I and x-y " is an integer "} , then prove that R is an equivalence relations.

Let S be a relation on the set R of all real numbers defined by S={(a ,\ b) in RxxR : a^2+b^2=1} . Prove that S is not an equivalence relation on R .

A relation R defined on the set of natural no as follows R={(x,y),x+5y=20,x, y in N }.Find in domain and range of R.

The relation R is defined on the set of natural numbers N as x is a factor of y where x, y in N. Then R is -