Let R be a relation on the set N be defined by x- y - x- y - N- 2 x-y-41- Then R isA- ReflexiveB- SymmetricC- TransitiveD- None of these

The correct option is D None of these On the set N of natural numbers, R = (x,y): x,y ∈ N , 2x + y = 41. Since (1,1) ∉ R as 2.1+1 = 3 41. So R is not reflexi ...

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Standard IX

Mathematics

Reflexive Relations

Let R be a re...

Question

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

Reflexive

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Symmetric

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Transitive

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None of these

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Solution

The correct option is D
None of these

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 $\neq$ 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 .

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

The correct option is D None of these On the set N of natural numbers, R = {(x,y): x,y ∈ N , 2x + y = 41}. Since (1,1) ∉ R as 2.1+1 = 3 ≠ 41. So R is not reflexive. (1,39) ∈ R But (39,1) ∉ R . So R is not symmetric (20,1) (1,39 ∈ R . But (20,39) ∉ R. So R is not transitive .