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 ...

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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.

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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 $x > z$ .

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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.