Relation R ={( x , y ): x , y ∈ z and x + y is even } is :

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1.Relation and Function

medium

The relation $R =\{( x , y ): x , y \in z$ and $x + y$ is even $\}$ is :

Areflexive and transitive but not symmetric

Breflexive and symmetric but not transitive

Can equivalence relation

Dsymmetric and transitive but not reflexive

(JEE MAIN-2025)

Solution

$R =\{( x , y ), x + y$ is even $x , y \in z \}$
reflexive $x+x=2 x$ even
symmetric of $x+y$ is even, then $(y+x)$ is also even
transitive of $x + y$ is even $\& y + z$ is even then $x+z$ is also even
So, relation is an equivalence relation.

Standard 12

Mathematics

Let $R$ be a reflexive relation on a finite set $A$ having $n$-elements, and let there be m ordered pairs in $R$. Then

normal

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medium

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medium

(JEE MAIN-2024)

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medium

Let $R$ be a relation defined on $N \times N$ by $(a, b) R(c, d) \Leftrightarrow a(b + c) = c(a + d).$ Then $R$ is

normal

The relation $R =\{( x , y ): x , y \in z$ and $x + y$ is even $\}$ is :

Solution

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