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.

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)}

Philoid · Accepted Answer

It is given that S = {a, b, c} and T = {1, 2, 3}

F: S → T is defined as:

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

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

Therefore, F is not invertible

⇒ F^-1 does not exists.