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36 votes
36 votes
Which logic statement represents this argument?If I work out every day and eat healthy, I will not get sick.p: I work out every dayq: I eat healthily r: I will get sick

Which logic statement represents this argument?If I work out every day and eat healthy-example-1
User Celin
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1 Answer

24 votes
24 votes

In this problem, we are trying to translate a given situation into logical notation.

We are given

p: I work out every day.

q: I eat healthily

r: I will get sick.

We are trying to translate "If I work out every day and eat healthily, I will not get sick."

We are essentially saying that if we do p and q, then r will not happen. Let's take a look at each part.

The notation for "and" is


\wedge

Therefore, we can group p and q together as


p\wedge q

Since these must happen together before reaching the conclusion, we should also include the parentheses:


(p\wedge q)

Next, we are saying that r will not happen. The notation for "not" is


\urcorner

But in your question, we need to use ~. So, we have the last part of the statement as


\text{ \textasciitilde}r

Since p and q imply ~r, we can write the entire statement as:


(p\wedge q)\rightarrow\text{ \textasciitilde }r

The correct answer is C.

User Jayfessenden
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3.7k points