Questions: Let p and q represent the following simple statements: p : I get an A. q : The chair is broken. Write the symbolic statement ~p ∧ q in words. Choose the correct sentence below. A. I do not get an A and the chair is broken. B. I do not get an A or the chair is broken. C. I get an A and the chair is not broken. D. I do not get an A and the chair is not broken.

Let p and q represent the following simple statements: p : I get an A. q : The chair is broken. Write the symbolic statement ~p ∧ q in words. Choose the correct sentence below. A. I do not get an A and the chair is broken. B. I do not get an A or the chair is broken. C. I get an A and the chair is not broken. D. I do not get an A and the chair is not broken.
Transcript text: Let $p$ and $q$ represent the following simple statements: $p$ : I get an $A$. $q$ : The chair is broken. Write the symbolic statement $\sim p \wedge q$ in words. Choose the correct sentence below. A. I do not get an A and the chair is broken. B. I do not get an A or the chair is broken. C. I get an A and the chair is not broken. D. I do not get an A and the chair is not broken.
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Solution

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Solution Steps

Step 1: Understand the given symbolic statement

The symbolic statement is \( \sim p \wedge q \). Here, \( \sim p \) represents the negation of \( p \), and \( \wedge \) represents the logical "and."

Step 2: Translate \( \sim p \) into words

Since \( p \) represents "I get an A," \( \sim p \) translates to "I do not get an A."

Step 3: Translate \( q \) into words

The statement \( q \) represents "The chair is broken," so \( q \) remains as "The chair is broken."

Step 4: Combine \( \sim p \) and \( q \) using \( \wedge \)

The logical "and" (\( \wedge \)) combines the two statements, so \( \sim p \wedge q \) translates to "I do not get an A and the chair is broken."

Step 5: Match the translated statement with the options

The correct sentence is:
A. I do not get an A and the chair is broken.

Final Answer

The correct answer is A.

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