True or False
If R = {(x,y) |x,y,`in{1,2,3,4,5} and x+y<5}`, then R = {(1,1),(1,2),(1,3),(2,1),(2,2),(3,1)}.

Let X = {1, 2, 3, 4, 5, 6, 7, 8, 9} . Let R_1 be a relation in 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} . Show that R_1 = R_2 .

True or false: The function F(x,y)=ysin(y/x)-x is a homogenous function of degree 1.

Let y be an element of the set A={1,2,3,4,5,6,10,15,30} and x_(1) , x_(2) , x_(3) be integers such that x_(1)x_(2)x_(3)=y , then the number of positive integral solutions of x_(1)x_(2)x_(3)=y is

True or false The region represented by {(x,y):x^2+y^2le9}cap{(x,y):x^2+y^2ge4) is convex.

True or false The line x=y=z lies in the plane x-2y+z-1=0.

An equilateral triangle has each of its sides of length 4 cm. If (x_(r),y_(r)) (r=1,2,3) are its vertices the value of |{:(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1):}|^2

Let A = (2,3,4,5,6,7,8,9). Let R be the relation on A defined by (x,y):x in A, y in A and x divides y .Find range of R^-1

Let A = {1, 2, 3, 4} and B = {x,y,z}. Let R be a relation from A into B defined by : R= {(1,x), (1,z), (3,x), (4,y)}. Find the domain and range of R.

If R is a relation on the set S = {1,2,3,4,5,6,7,8,9) given by xR y ,y = 3x, then R = is