b. Let \( \mathrm{p}: \) I am stressed. Let \( \mathrm{q}: \) I went to yoga. Let r : I meditated. Given the statement "If I am not stressed, then I went to yoga or I meditated." The conditional statement is Op \( \rightarrow \sim(q \vee r) \) \( O \sim p \rightarrow \sim(q \vee r) \) \( O \sim p \rightarrow(q \vee r) \) \( O p \rightarrow(q \vee r) \)

To analyze the given statement "If I am not stressed, then I went to yoga or I meditated," we need to break it down into its logical components using the provided symbols: - Let \( p \): I am stressed. - Let \( q \): I went to yoga. - Let \( r \): I meditated. The statement can be interpreted as follows: 1. "I am not stressed" translates to \( \sim p \). 2. "I went to yoga or I meditated" translates to \( q \vee r \). Now, the entire statement "If I am not stressed, then I went to yoga or I meditated" can be expressed in logical form as: \[ \sim p \rightarrow (q \vee r) \] This means that if I am not stressed (\( \sim p \)), then it follows that I either went to yoga (\( q \)) or I meditated (\( r \)). Now, let's evaluate the options provided: 1. \( O p \rightarrow \sim(q \vee r) \) - This is incorrect because it suggests that if I am stressed, then I did not go to yoga and did not meditate. 2. \( O \sim p \rightarrow \sim(q \vee r) \) - This is incorrect because it suggests that if I am not stressed, then I did not go to yoga and did not meditate. 3. \( O \sim p \rightarrow (q \vee r) \) - This is correct as it matches our derived logical expression. 4. \( O p \rightarrow (q \vee r) \) - This is incorrect because it suggests that if I am stressed, then I went to yoga or I meditated. Thus, the correct conditional statement is: \[ O \sim p \rightarrow (q \vee r) \]