एक सम्बन्ध `R={(x,y):x,y in A " और" x lt y}` समुच्चय A={1,2,3,4,5} पर परिभाषित है, सम्बन्ध R है -

Let R ={(x,y) : x,y in A, x+y=5} , where A= {1,2,3,4,5}. Then :

Let R={(x,y):x,y in A,x+y=5} where A= { 1,2,3,4,5} then

Let R={(x,y):x,yepsilonA,x+y=5} where A={1,2,3,4,5} then R is

Let R={(x,y):x,yepsilonA,x+y=5} where A={1,2,3,4,5} then R is

Let R be a relation on the set of natural numbers ,defined as R ={(x,y):x+2y=20, x,y varepsilon N} and x varepsilon {1,2,3,4,5} .Then ,the range of 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} defined 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}.

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 .

If R ={(x,y) :x is an integer and |x| lt 3 "and" y=|x-3|} then the range of R is

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}