A relation R on A -1-2-3-4 is defined as x R y if x divides y- Then R isA- equivalenceB- symmetric and transitiveC- reflexive and symmetricD- reflexive and transitive

The correct option is D reflexive and transitive xϵ A ⇒ x divides x x,y,z ϵ A and if x divides y, y divides z ⇒ x divides z ∴ R is reflexive and transitive ...

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Standard XII

Mathematics

Transitive Relations

A relation R ...

Question

A relation R on A = {1,2,3,4} is defined as x R y if x divides y. Then R is

equivalence

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symmetric and transitive

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reflexive and symmetric

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reflexive and transitive

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Solution

The correct option is D
reflexive and transitive

$x ϵ A \Rightarrow x d i v i d e s x x, y, z ϵ A a n d i f x d i v i d e s y, y d i v i d e s z \Rightarrow x d i v i d e s z ∴ R i s r e f l e x i v e a n d t r a n s i t i v e$

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A relation R on A = {1,2,3,4} is defined as x R y if x divides y. Then R is

The correct option is D reflexive and transitive xϵA⇒x divides xx,y,z ϵA and if x divides y, y divides z⇒x divides z∴R is reflexive and transitive

The correct option is D
reflexive and transitive

$x ϵ A \Rightarrow x d i v i d e s x x, y, z ϵ A a n d i f x d i v i d e s y, y d i v i d e s z \Rightarrow x d i v i d e s z ∴ R i s r e f l e x i v e a n d t r a n s i t i v e$