Which one of the following relations on `R` is equivalence relation `x R_1y |x|=|y|` b. `x R_2y xgeqy` c. `x R_3y x|x y(xd i v i d e sy)|` d. `x R_4y x

Which of the relations R on the set of the real numbers is an equivalence relation? (a).x R y if |x|=|y|

Prove that the following relation R in Z of integers is an equivalence relation R = {(x, y): x-y is an integer}

Prove that the following relation R in Z of integers is an equivalence relation : R = [ (x, y) : 3x- 3y is an integer}

Prove that the following relation R in Z of integers is an equivalence relation : R = [ (x, y) : x - y is an integer}

Prove that the following relation R in Z of integers is an equivalence relation : R = [ (x, y) : 2x - 2y is an integer}

In the set Z of all integers, which of the following relation R is not an equivalence relation? x\ R\ y : if xlt=y (b) x\ R\ y : if x=y (c) x\ R\ y : if x-y is an even integer (d) x\ R\ y : if x=y (mod 3)

In the set Z of all integers, which of the following relation R is not an equivalence relation? x\ R\ y : if xlt=y (b) x\ R\ y : if x=y (c) x\ R\ y : if x-y is an even integer (d) x\ R\ y : if x=y (mod 3)

Which one of the following is not a function? {(x , y): x , y in R , x^2=y} b. {(x , y): x , y in R , y^2=x} c. {(x , y): x , y in R , x=y^3} d. {(x , y): x , y in R , y=x^3}

Let R be the real line. Consider the following subsets of the plane RxxR . S""=""{(x ,""y)"":""y""=""x""+""1""a n d""0""<""x""<""2},""T""=""{(x ,""y)"":""x-y"" is an integer }. Which one of the following is true? (1) neither S nor T is an equivalence relation on R (2) both S and T are equivalence relations on R (3) S is an equivalence relation on R but T is not (4) T is an equivalence relation on R but S is not

Let R be the real line. Consider the following subsets of the plane RxxR . S""=""{(x ,""y)"":""y""=""x""+""1""a n d""0""<""x""<""2},""T""=""{(x ,""y)"":""x-y"" is an integer }. Which one of the following is true? (1) neither S nor T is an equivalence relation on R (2) both S and T are equivalence relations on R (3) S is an equivalence relation on R but T is not (4) T is an equivalence relation on R but S is not