function f: {a, b, c} -> {1, 2 ,3} defined by f(a) = 1, f(b) = 1, f(c) = 2

if ~f(y) represents inverse function

is ~f({1,3}) = {a, b} correct? or should it be ~f({1}) = {a, b}

the former is printed in the book and i'm kinda confused why ~f({1, 3}) gives {a,b} since ~f({3}) gives NIL.

Appreciate any clarification

Thank you