Questions: Consider statements p and q. p : We sell carrots at the market. q : We sell berries at the market. For part (a), fill in the symbolic form. For part (b), choose the descriptive form. Descriptive form Symbolic for (a) If we do not sell berries at the market, then we sell carrots at the market. (b) (Choose one) p ↔ ~q

Consider statements p and q. p : We sell carrots at the market. q : We sell berries at the market. For part (a), fill in the symbolic form. For part (b), choose the descriptive form. Descriptive form Symbolic for (a) If we do not sell berries at the market, then we sell carrots at the market. (b) (Choose one) p ↔ ~q
Transcript text: Consider statements $p$ and $q$. $p$ : We sell carrots at the market. $q$ : We sell berries at the market. For part (a), fill in the symbolic form. For part (b), choose the descriptive form. Descriptive form Symbolic for (a) If we do not sell berries at the market, then we sell carrots at the market. $\square$ (b) (Choose one) \[ p \leftrightarrow \sim q \]
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Solution

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Solution Steps

To solve this problem, we need to translate the given statements into symbolic logic. For part (a), we need to express the statement "If we do not sell berries at the market, then we sell carrots at the market" using the symbols for $p$ and $q$. For part (b), we need to choose the correct symbolic form that matches the descriptive form given.

Solution Approach
  1. Identify the logical structure of the statement in part (a). It is a conditional statement, which can be represented as $\sim q \rightarrow p$.
  2. For part (b), compare the given symbolic forms with the descriptive form to find the correct match.
Step 1: Symbolic Form for Part (a)

The statement "If we do not sell berries at the market, then we sell carrots at the market" can be expressed in symbolic form as: \[ \sim q \rightarrow p \]

Step 2: Choosing the Correct Symbolic Form for Part (b)

We need to match the descriptive form with the correct symbolic representation. The options provided are:

  1. \( p \leftrightarrow \sim q \)
  2. \( \sim q \rightarrow p \)

The descriptive form "If we do not sell berries at the market, then we sell carrots at the market" corresponds to the symbolic form \( \sim q \rightarrow p \).

Final Answer

For part (a), the symbolic form is \( \sim q \rightarrow p \). For part (b), the correct symbolic form is \( \sim q \rightarrow p \).

Thus, the answers are: \[ \boxed{\text{Part (a): } \sim q \rightarrow p} \] \[ \boxed{\text{Part (b): } \sim q \rightarrow p} \]

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