#### Question

Which of the following functions from *A* to *B* are one-one and onto?

*f*_{2} = {(2, *a*), (3, *b*), (4, *c*)} ; *A* = {2, 3, 4}, *B* = {*a*, *b*, *c*}

#### Solution

*f*_{2} = {(2, *a*), (3, *b*), (4, *c*)} ; *A* = {2, 3, 4}, *B* = {*a*, *b*, *c*}

**Injectivity:***f*_{2}* *(2)* = a**f*_{2}* *(3)* = b**f*_{2}* *(4)* = c*

⇒ Every element of A has different images in B.

So, f_{2} is one-one.

**Surjectivity:**

Co-domain of *f*_{2} = {*a*, *b*, *c*}

Range of *f*_{2} = set of images = {*a*, *b*, *c*}

⇒ Co-domain = range

So, *f*_{2} is onto.

Is there an error in this question or solution?

Solution Which of the Following Functions From A To B Are One-one and Onto? F2 = {(2, A), (3, B), (4, C)} ; A = {2, 3, 4}, B = {A, B, C} Concept: Types of Functions.