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  • Confused! kindly explain, - Sets, Relations and Functions - JEE Main

Consider the following two binary relations on the setA=\left \{ a,b,c \right \}:R_{1}=\left \{ \left ( c,a \right ) ,\left ( b,b \right ),\left ( a,c \right ),\left ( c,c \right ),\left ( b,c \right ),\left ( a,a \right )\right \}

and R_{2}=\left \{ \left ( a,b \right ) ,\left ( b,a \right ),\left ( c,c \right ),\left ( c,a\right ),\left ( a,a \right ),\left ( b,b \right ),\left ( a,c \right )\right \}.

Then :

  • Option 1)

     both R1 and R2 are not symmetric.

     

     

     

  • Option 2)

     R1 is not symmetric but it is transitive.

  • Option 3)

     R2 is symmetric but it is not transitive.

  • Option 4)

     both R1 and R2 are transitive.

 

Answers (2)

best_answer

As we learned 

 

REFLEXIVE RELATION -

A relation R in A is said to be reflexive,  if a R a ,∀ a ∈ A

-

 

 

SYMMETRIC RELATION -

A relation R in A is said to be symmetric, if a R b ⇒ b R a,∀ a,b ∈ A

-

 

 

TRANSITIVE RELATION -

A relation R in A is said to be transitive, if a R b and b R c ⇒ a R c ∀ a,b,c ∈ A

-

 

 

R_{1}:\left \{ \left ( c,a \right )\left ( a,b \right )\left ( a,a \right ) \left ( c,c \right )\left ( b,c \right )\left ( a,a \right )\right \}

R1 is not reflexive since (b,b) is not present. 

(c,a) and (a,c) are present ; 

(a,b) is here but (b,a). So R1 is not symmetric.

Also, it is not transitive. 

similarlly, R2 is symmetric and not transitive.  

 

 

 


Option 1)

 both R1 and R2 are not symmetric.

 

 

 

Option 2)

 R1 is not symmetric but it is transitive.

Option 3)

 R2 is symmetric but it is not transitive.

Option 4)

 both R1 and R2 are transitive.

Posted by

Himanshu

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