Related questions with answers
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.
Solution
VerifiedThe 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: $\text{\textcolor{#c34632}{If a person is not voting, then he or she is not a citizen.}}$
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