Question

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

Answer 1

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.