Use the statements below to convert the argument into symbolic form. p: I eat salads for lunch for a month. \( \mathrm{q}: \) I lose ten pounds. I eat salads for lunch for a month and I lose ten pounds. I lose ten pounds. Therefore, I ate salads for lunch for a month. Which symbolic form represents the argument? \[ p \vee q \] \( \sim p \) \( \therefore q \) \( p \wedge q \) \( \frac{q}{\therefore p} \) \( p \rightarrow q \) \( \frac{q}{\therefore p} \) \[ p \rightarrow q \] \( \sim q \) \( \therefore \sim p \) \[ p \vee q \] \( p \) \[ \therefore \sim q \] \[ p \rightarrow q \] \( \frac{p \vee r}{\therefore \sim q} \) \[ p \rightarrow q \] \( \frac{\sim p}{\therefore \sim q} \) \( p \rightarrow q \) \( \frac{\sim p \wedge r}{\therefore \sim q} \)
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Beyond the Answer
In this argument, you're trying to establish a cause-and-effect relationship between eating salads for lunch and losing weight. Starting with the premises, you state that eating salads for a month and losing weight is true, as well as the conclusion. This can be represented symbolically as follows: \( p \wedge q \) for the conjunction of the statements (I eat salads and I lose weight), leading to the conclusion \( \frac{q}{\therefore p} \) that if I lost weight, then I must have eaten salads. To put it simply, the argument can be summarized symbolically as: 1. \( p \wedge q \) (I eat salads for lunch and I lose ten pounds) 2. Therefore, \( \frac{q}{\therefore p} \) (Since I lost ten pounds, therefore I ate salads for lunch).
