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 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

For which of the following,y can be a function of x,(x in R,y in R)?

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

If R={(x,y):x,y in Z and x^(2)+y^(2)=49} is a relation,then which of the following element is not present in range of R?

Let Z be the set of all integers. A relation R is defined on Z by xRy to mean x-y is divisible by 5. Show that R is an equivalence relation on Z.

Let Z be the set of all integers. A relation R is defined on Z by xRy to mean x-y is divisible by 5. Show that R is an equivalence relation on Z.

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

Find the inverse relation R^(-1) in each of the following cases: R:{(x,y):x,y in N,x+2y=8}

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

R is a relation on N given by R={(x,y):4x+3y=20}. Which of the following belongs to R?