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  • I need help with - Sets, Relations and Functions - JEE Main-5

If R1 and R2 be relations on \left \{ 1,2,3,4,5 \right \} defined by 

R_{1}=\left \{ \left ( 1,1 \right ) ,\left ( 2,3 \right ),\left ( 2,4 \right ),\left ( 3,5 \right ),\left ( 5,2 \right )\left ( 5,5 \right )\right \}

R_{1}=\left \{ \left ( 1,1 \right ) ,\left ( 2,2 \right ),\left ( 2,3 \right ),\left ( 2,5 \right ),\left ( 4,3 \right )\left ( 5,5 \right )\right \}

which of the following is not an elements of R_{2}\cdot R_{1} ?

  • Option 1)

    \left ( 1,2 \right )

     

  • Option 2)

    \left ( 2,3 \right )

  • Option 3)

    \left ( 4,5 \right )

  • Option 4)

    \left ( 5,5 \right )

 

Answers (1)

best_answer

As we learned 

 

Composition of relation -

Let R & S be 2 relation from set A to B and B to C respectively. If \left ( a,c \right )\in SoR,

Then there exists b \in B  such that \left ( a,b \right )\in R and \left ( b,c \right )\in S

-

 

 R_{1}\cdot R_{2}=\left \{ \left ( 1,1 \right ),\left ( 2,3 \right ),\left ( 2,4 \right ),\left ( 2,5 \right ),\left ( 4,5 \right ) ,\left ( 5,5 \right )\right \}

 


Option 1)

\left ( 1,2 \right )

 

Option 2)

\left ( 2,3 \right )

Option 3)

\left ( 4,5 \right )

Option 4)

\left ( 5,5 \right )

Posted by

Himanshu

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