#### Please Solve RD Sharma Class 12 Chapter Function Exercise 2.4 Question 22 Maths Textbook Solution.

Bijection

Given:

$A=\left \{ 1,2,3,4 \right \},B=\left \{ a,b,c,d \right \}$

Hint:

Bijection should fulfil the one-one, onto condition.

Solution:

$f_{1}=\left \{ \left ( 1,a \right ),\left (2,b \right ),\left ( 3,c\right ) ,\left ( 4,d \right )\right \}$

$f_{1}^{-1}=\left \{ \left ( a,1 \right ),\left (b,2 \right ),\left ( c,3\right ) ,\left ( d,4\right )\right \}$

$f_{2}=\left \{ \left ( 1,b \right ),\left (2,a \right ),\left ( 3,c\right ) ,\left ( 4,d \right )\right \}$

$f_{2}^{-1}=\left \{ \left ( b,1 \right ),\left (a,2 \right ),\left ( c,3\right ) ,\left ( d,4\right )\right \}$

$f_{3}=\left \{ \left ( 1,a \right ),\left (2,b \right ),\left ( 4,c\right ) ,\left ( 3,d \right )\right \}$

$f_{3}^{-1}=\left \{ \left ( a,1 \right ),\left (b,2 \right ),\left ( c,4\right ) ,\left ( d,3 \right )\right \}$

$f_{4}=\left \{ \left ( 1,b \right ),\left (2,a \right ),\left ( 4,c\right ) ,\left ( 3,d\right )\right \}$

$f_{4}^{-1}=\left \{ \left ( b,1 \right ),\left (a,2 \right ),\left ( c,4\right ) ,\left ( d,3\right )\right \}$

Clearly, all these are bijections because they are one-one and onto.