Let $S$ Be the Set of All Strings in 0's and 1's

question 17

Essay

Let $S$ be the set of all strings in 0's and 1's, and define a function $g$ : $S \longrightarrow \mathbf { Z }$ as follows: for each string $s$ in $S$ ,
$g ( s ) =$ the number of 1's in $s$ minus the number of 0 's in $s .$
(a) What is $g ( 101011 ) ? g ( 00100 )$ ?
(b) Is $g$ one-to-one? Prove or give a counterexample.
(c) Is $g$ onto? Prove or give a counterexample.

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Definitions:

Competition

The activity or condition of striving to gain or win something by defeating or establishing superiority over others.

Confrontation

A direct engagement or encounter between individuals or groups over a disagreement or conflict.

Menarche

The first occurrence of menstruation in a female, marking the beginning of reproductive capability.

Euphemisms

Mild or indirect words or expressions used in place of ones considered harsh or blunt when referring to something unpleasant or embarrassing.