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

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 of the following relations is not symmetric? R_(1), on R defined by (x,y)in R_(1)hArr1+xy>0 for all x,y in R

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={(x,y):x^(2)+y^(2)=1,x,y in R} be a relation in R. Then the relation R is

Determine whether each of the following relations are reflexive, symmetric and transitive: (i) Relation R in the set A = {1, 2, 3, ..., 13, 14} defined as R = {(x, y) : 3x – y = 0} (ii) Relation R in the set N of natural numbers defined as R = {(x, y) : y = x + 5 and x lt 4} (iii) Relation R in the set A = {1, 2, 3, 4, 5, 6} as R = {(x, y) : y is divisible by x } (iv) Relation R in the set Z of all integers defined as R = {(x, y) : x – y is an integer} (v) Relation R in the set A of human beings in a town at a particular time given by (a) R = {(x, y) : x and y work at the same place} (b) R = {(x, y) : x and y live in the same locality} (c) R = {(x, y) : x is exactly 7 cm taller than y } (d) R = {(x, y) : x is wife of y } (e) R = {(x, y) : x is father of y }

For x,y in I, the relation R is defined by xRy f and only if x<=y then R is

Let R be a relation on N defined by R={(x,y):x+2y=8). Then domain of R is

Let R be a relation on N defined by R={(x,y):2x+y=10}, then domain of R is

A relation R:Zrarr2 is such that R={(x,y)//y=2x+1) is a