Let `R={(x ,\ y):|x^2-y^2|<1}` be a relation on set `A={1,\ 2,\ 3,\ 4,\ 5}` . Write `R` as a set of ordered pairs.

If R={(x ,\ y): x^2+y^2lt=4; x ,\ y in Z} is a relation on Z , write the domain of R .

Let P={(x,y)|x^(2)+y^(2)=1,x,yinR} . Then, R, is

Which of the following are function: {(x , y): y^2=x , x , y in R} b. {(x , y): y=|x|, x , y in R} c. {(x , y): x^2+y^2=1, x , y in R} d. {(x , y): x^2-y^2=1, x , y in R}

Let R={(x , y): x , y in Z ,\ y=2x-4} If\ (a,-2)\ a n d\ (4, b^2) in R , then write the values of a and b.

Let X={1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7,\ 8,\ 9} , Let R_1 be a relation on X given by R_1={(x ,\ y): x-y is divisible by 3} and R_2 be another relation on X given by R_2={(x ,\ y):{x ,\ y}sub{1,\ 4,\ 7} or {x ,\ y}sub{2,\ 5,\ 8} or {x ,\ y}sub{3,\ 6,\ 9}}dot Show that R_1=R_2 .

Let R="{"x , y")": x , y in R ,x^2+y^2lt=25} and R^(prime)={(x , y): x , y in R , ygeq4/9x^2}dot Then find the domain and range of RnnR^(prime)dot

Let R = {(x, y) : x, y in N and x^2-4xy+3y^2 = 0} , where N is the set of all natural numbers. Then the relation R is

Let f (x,y)= x^(2) - y^(2) and g (x,y)=2xy. such that (f ( x,y))^(2) -(g (x,y))^(2)=1/2 and f (x,y) . G(x,y) =(sqrt3)/(4) Find the number of ordered pairs (x,y) ?

The relation R given by {(x, y):x^(2)-3xy+2y^(2)=0, AA x, y in R} is

Let S={(x,y)|x,y in R, x^2+y^2-10x+16=0} . The largest value of y/x can be put in the form of m/n where m, n are relatively prime natural numbers, then m^2+n^2=