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

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

Answers (1)

Answer:

                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.

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