The following defines a relation on N- R-x- y-x- y- N-Determine whether it is reflexive- symmetric and transitive-

The given relation R on the set of natural (N) number is not a reflexive as (x,x)∉R since xx for any x∈ N .Again the relation is no ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Reflexive Relations

The following...

Question

The following defines a relation on $N$ :
$R = {x > y, x, y \in N}$ .
Determine whether it is reflexive, symmetric and transitive.

Open in App

Solution

The given relation $R$ on the set of natural $(N)$ number is not a reflexive as $(x, x) \notin R$ since $x ≯ x$ for any $x \in N$ .
Again the relation is not symmetric as $(3, 2) \in R$ but $(2, 3) \notin R$ .
But the relation is transitive as if $(x, y) \in R, (y, z) \in R \Rightarrow (x, z) \in R$ for all $x, y, z \in N$ . Since $x > y, y > z$ gives $x > z$ .

Suggest Corrections

Similar questions

Determine whether each of the following relations are reflexive, symmetric and transitive:
(ii) Relation R in the set N of natural numbers defined as
R = {(x, y): y = x + 5 and x < 4}

Determine whether the following relation is reflexive, symmetric and transitive

Relative

R

in the set

N

of natural numbers defined as

R = {(x, y) : y = x + 5 a n d x < 4}

enter 1-Reflexive
2-Symmetric
3-Transitive
4-Equivalence
5-None

Q. Determine whether the relation

R

in the set

A = {1, 2, 3, . . . . ., 13, 14}

defined as

R = {(x, y) : 3 x - y = 0}

, is reflexive, symmetric and transitive.

Q. Determine whether the following relation is reflexive, transitive and symmetric :
R = {(x,y) : x and y work at the same place }

Q. Let

R

be a relation defined on

N

R = {(x, y) | x, y \in N, 2 x + y = 41} .

Then

R

Join BYJU'S Learning Program

The following defines a relation on N:R={x>y,x,y∈N}.Determine whether it is reflexive, symmetric and transitive.

The given relation R on the set of natural (N) number is not a reflexive as (x,x)∉R since x≯x for any x∈N.Again the relation is not symmetric as (3,2)∈R but (2,3)∉R.But the relation is transitive as if (x,y)∈R,(y,z)∈R⇒(x,z)∈R for all x,y,z∈N. Since x>y,y>z gives x>z.

The following defines a relation on $N$ :
$R = {x > y, x, y \in N}$ .
Determine whether it is reflexive, symmetric and transitive.