Let `f : {1, 2, 3}->{a , b , c}`be one-one and onto function given by `f (1) = a`, `f (2) = b`and `f (3) = c`. Show that there exists a function `g : {a , b , c}->{1, 2, 3}`such that `gof=I_x`and `fog=I_y`

Explanation

To solve the problem, we need to show that there exists a function \( g : \{a, b, c\} \to \{1, 2, 3\} \) such that the composite functions \( g \circ f = I_X \) and \( f \circ g = I_Y \), where \( I_X \) and \( I_Y \) are the identity functions on the respective sets.

### Step 1: Understand the function \( f \)
We are given the function \( f : \{1, 2, 3\} \to \{a, b, c\} \) defined as:
- \( f(1) = a \)
- \( f(2) = b \)
- \( f(3) = c \)

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