Let N be the set of natural numbers and relation R on N be defined by `R={(x,y):x,y in N, x+4y=10}` check whether R is reflexive , symmetric and transitive.

Let Q be the set of rational number and R be the relation on Q defined by R={(x,y):x,y in Q , x^(2)+3y^(2)=4xy} check whether R is reflexive, symmetric and transitive.

Let R be a relation on the set N be defined by {(x,y)|x,yepsilonN,2x+y=41} . Then prove that the R is neither reflexive nor symmetric and nor transitive.

Let N be the set of all natural niumbers and let R be a relation in N , defined by R={(a,b):a" is a factor of b"}. then , show that R is reflexive and transitive but not symmetric .

Let N be the set of all natural numbers and let R be relation in N. Defined by R={(a,b):"a is a multiple of b"}. show that R is reflexive transitive but not symmetric .

Let N be the set of natural numbers and the relation R be defined on N such that R={(x,y):y=2x,x,y in N} What is the domain,codomain and range of R? Is this relation a function?

Let N be the set of all natural numbers and we define a relation R={(x ,y):x, y in N , x+y is a multiple of 5} then the relation R is

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

Let N be the set of natural numbers and a relation R on N be defined by R = { (x, y) in N xx N : x^(3) - 3 x ^(2) y - xy ^(2) + 3y ^(3) = 0 } . Then the relation R is :