Question

let R =,{(xy):X+3y=0,y€N y is R a relation on N
​

Answer 1

R={(x,y):x

2

−4xy+3y

2

=0,x,y∈N}.

Let x∈N.x

2

−4xx+3x

2

=4x

2

−4x

2

=0

∴(x,x)∈R.

∴R is reflexive

We have (3)

2

−4(3)(1)+3(1)

2

=9−12+3=0

∴(3,1)∈R.

Also (1)

2

−4(1)(3)+3(3)

2

=1−12+27=16



=0

∴(1,3)∈

/

R.

∴R is not symmetric.

(9,3)∈R because

(9)

2

−4(9)(3)+3(3)

2

=81−108+27=0

Also (3,1)∈R because

(3)

2

−4(3)(1)+3(1)

2

=9−12+3=0

Now, (9,1)∈R if (9)

2

−4(9)(1)+3(1)

2

=0

if 81−36+3=48



=0,

which is not so.

∴(9,3),(3,1)∈R and (9,1)∈

/

R

∴R is not transitive.