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Question 22 \( 0 / 1 \) pt 3 For the simple statements \( p: \) The water is warm. \( q \) : The sun is shining. \( r \) : We go swimming. Match each compound statement to its symbolic form. \( \square \) If the sun is shining then the water is warm, or we go swimming. - - The water is warm or the sun is shining, and we don't go swimming. \( -\hat{\text { If }} \) If the sun is shining, then the water is warm if and only if we go swimming. \( -\hat{\sim} \) If we don't go swimming, then the sun is shining and the water is warm. - - If the sun is shining then we go swimming, and the water is warm. - - If the water is not warm, then the sun is shining or we go swimming. \( -\uparrow \) The sun is shining if and only if the water is warm, and we go swimming. - If the sun is shining and we go swimming, then the water is warm. \( -\quad \) The water is not warm, and the sun is shining or we go swimming. \( -\quad \) The water is warm and the sun is shining, or we go swimming. a. \( q \rightarrow(p \leftrightarrow r) \) b. \( (p \wedge q) \vee r \) c. \( \sim r \rightarrow(q \wedge p) \) d. \( (p \vee q) \wedge \sim r \) e. \( (q \rightarrow p) \vee r \) f. \( \sim p \rightarrow(q \vee r) \) g. \( (q \leftrightarrow p) \wedge r \) h. \( (q \wedge r) \rightarrow p \) i. \( (q \rightarrow r) \wedge p \) j. \( \sim p \wedge(q \vee r) \)

Ask by Mccoy Frank. in the United States
Mar 11,2025

Solución de inteligencia artificial de Upstudy

Respuesta verificada por el tutor

Responder

1. \( q \rightarrow (p \vee r) \) → **e** 2. \( (p \vee q) \wedge \sim r \) → **d** 3. \( q \rightarrow (p \leftrightarrow r) \) → **a** 4. \( \sim r \rightarrow (q \wedge p) \) → **c** 5. \( (q \rightarrow r) \wedge p \) → **i** 6. \( \sim p \rightarrow (q \vee r) \) → **f** 7. \( \sim p \wedge (q \vee r) \) → **j** 8. \( (p \wedge q) \vee r \) → **b**

Solución

1. \( q \rightarrow (p \vee r) \) is equivalent to   \( (q\rightarrow p) \vee r \)  →  option **e** 2. \( (p \vee q) \wedge \sim r \)  →  option **d** 3. \( q \rightarrow (p \leftrightarrow r) \)  →  option **a** 4. \( \sim r \rightarrow (q \wedge p) \)  →  option **c** 5. \( (q \rightarrow r) \wedge p \)  →  option **i** 6. \( \sim p \rightarrow (q \vee r) \)  →  option **f** 7. \( \sim p \wedge (q \vee r) \)  →  option **j** 8. \( (p \wedge q) \vee r \)  →  option **b**

Respondido por UpStudy AI y revisado por un tutor profesional

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The Deep Dive

Let’s get diving into the symbolic depths of logic! The statement “If the sun is shining then the water is warm, or we go swimming” corresponds to **e. \( (q \rightarrow p) \vee r \)**. This captures the essence of either basking in warmth or making those splashes! Next up, “The water is warm or the sun is shining, and we don't go swimming” matches with **d. \( (p \vee q) \wedge \sim r \)**. It perfectly reflects a cheerful day spent contemplating warmth without a leap into the water!

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