Let R be a relation on set N be defined by {(x, y)| x, y ∈ N, 2x + y = 41} . Then R is

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1.Relation and Function

easy

Let $R$ be a relation on the set $N$ be defined by $\{(x, y)| x, y \in N, 2x + y = 41\}$. Then $R$ is

A

Reflexive

B

Symmetric

C

Transitive

D

None of these

Solution

(d) On the set $N$ of natural numbers,

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

Since $(1,1) \notin R$ as $2.1 + 1 = 3 \ne 41$. So, $R$ is not reflexive.

$(1,\,39) \in R$ but $(39,\,1) \notin R$. So $R$ is not symmetric $(20, 1)$

$(1, 39 \in R$. But $(20,39) \notin R$, So $R$ is not transitive.

Standard 12

Mathematics

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