#### Question

Let *S* = {*a*, *b*, *c*} and *T* = {1, 2, 3}. Find F^{−1} of the following functions F from *S* to *T*, if it exists.

*F* = {(*a*, 2), (*b*, 1), (*c*, 1)}

#### Solution

F: *S* → *T* is defined as:

F = {(*a*, 2), (*b*, 1), (*c*, 1)}

Since F (*b*) = F (*c*) = 1, F is not one-one.

Hence, F is not invertible i.e., F^{−1} does not exist.

Is there an error in this question or solution?

Solution Let S = {A, B, C} And T = {1, 2, 3}. Find F−1 Of the Following Functions F From S To T, If It Exists. F = {(A, 2), (B, 1), (C, 1)} Concept: Types of Functions.