Express each statement in “if... then” form. (More than one correct wording in “if... then” form may be possible.) Then write the statement’s converse, inverse, and contrapositive. Being a citizen is a necessary condition for voting.

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The conditional statement in the form `` $q$ is necessary for $p$ .'' can be written as $p\to q$ . So, a possible conditional form of the statement is: $\text{\textcolor{#c34632}{If a person is a citizen, then he or she is voting.}}$

Write the simple statements and their negations:

$p:$ A person is a citizen.
$\sim p:$ A person is not a citizen.
$q:$ A person is voting.
$\sim q:$ A person is not voting.

so that the statement is written as:

\color{#4257b2}p\to q

The $\textbf{converse}$ of $p\to q$ (If $p$ , then $q$ .) is $\color{#4257b2}q\to p$ (If $q$ , then $p$ .) so we write: $\text{\textcolor{#c34632}{If a person is voting, then he or she is a citizen.}}$

The $\textbf{inverse}$ of $p\to q$ (If $p$ , then $q$ .) is $\color{#4257b2}\sim p\to \sim q$ (If not $p$ , then not $q$ .) so we write: $\text{\textcolor{#c34632}{If a person is not a citizen, then he or she is not voting.}}$

The $\textbf{contrapositive}$ of $p\to q$ (If $p$ , then $q$ .) is $\color{#4257b2}\sim q\to \sim p$ (If not $q$ , then not $p$ .) so we write: $\text{\textcolor{#c34632}{If a person is not voting, then he or she is not a citizen.}}$