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# 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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Answered 2 years ago
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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: $\text{\textcolor{#c34632}{If a person is not voting, then he or she is not a citizen.}}$

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