# Correctness of a sample function

• Jun 25th 2006, 08:05 AM
terencetham
Correctness of a sample function
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
• Jun 25th 2006, 11:32 AM
CaptainBlack
Quote:

Originally Posted by terencetham
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

$
f^{-1}(\{1,3\})=f^{-1}(\{1\})\cup f^{-1}(\{3\})=\{a,b\}\cup \emptyset=\{a,b\}
$

where $\emptyset$ denotes the empty set, and so for any set $A$, $A \cup \emptyset=A$

RonL