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Select the correct answer.

Which logic statement represents this argument?

If I work out every day and eat healthily, I will not get sick.

[tex]\[
\begin{align*}
p &: \text{I work out every day.} \\
q &: \text{I eat healthily.} \\
r &: \text{I will get sick.}
\end{align*}
\][/tex]

A. [tex]\((p \wedge q) \rightarrow r\)[/tex]
B. [tex]\(p \wedge (q \rightarrow \sim r)\)[/tex]
C. [tex]\((p \wedge q) \rightarrow \sim r\)[/tex]
D. [tex]\((p \vee q) \rightarrow \sim r\)[/tex]
E. [tex]\(\sim(p \vee q) \rightarrow r\)[/tex]



Answer :

GinnyAnswer
To translate the given argument into a formal logic statement, we need to analyze the components of the statement:

The argument is:
"If I work out every day and eat healthily, I will not get sick."

Given:
- [tex]\(\rho\)[/tex] ([tex]\(p\)[/tex]): I work out every day.
- [tex]\(q\)[/tex]: I eat healthily.
- [tex]\(r\)[/tex]: I will get sick.

Let's break down the statement:
1. "If I work out every day and eat healthily" can be represented as [tex]\(p \wedge q\)[/tex].
2. "I will not get sick" indicates the negation of [tex]\(r\)[/tex], which is [tex]\(\sim r\)[/tex].

Putting these together, the statement:
"If I work out every day and eat healthily, I will not get sick" translates to:
[tex]\((p \wedge q) \rightarrow \sim r\)[/tex]

Therefore, the correct answer is:
C. [tex]\((p \wedge q) \rightarrow \sim r\)[/tex]

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