Login
Premium
Home Question Bank Other
Question
upstudy study bank question image url

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

Upstudy AI Solution

Tutor-Verified Answer

Answer

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**

Solution

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**

Answered by UpStudy AI and reviewed by a Professional Tutor

error msg
Explain
Simplify this solution

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!

Related Questions

Given the following maximum problem: Maximize: \( \quad P=8 x_{1}+4 x_{2} \) Subject to the following constraints: \[ \left\{\begin{array}{l} x_{1}+x_{2} \leq 2 \\ 2 x_{1}+5 x_{2} \leq 8 \\ x_{1} \geq 0 \\ x_{2} \geq 0 \end{array}\right. \] the Initial Simplex Tableau can be formatted in this form: \[ \left[\begin{array}{cccccc} P & x_{1} & x_{2} & s_{1} & s_{2} & R H S \\ a_{11} & a_{12} & a_{13} & a_{14} & a_{15} & a_{16} \\ a_{21} & a_{22} & a_{23} & a_{24} & a_{25} & a_{26} \\ \hline & & & & & \\ a_{31} & a_{32} & a_{33} & a_{34} & a_{35} & a_{36} \end{array}\right] \] In each box below, enter the appropriate value that must replace each of the letters \( a_{11} \) through \( a_{36} \) in the above tableau.
Other United States Mar 12, 2025
3. Let \( A=\{b, c, d\} \) and \( B=\{a, b\} \). Find the following: (a) \( (A \times B) \cap(B \times B) \) (b) \( (A \times B) \cup(B \times B) \) (c) \( \mathcal{P}(A) \cap \mathcal{P}(B) \) (d) \( \mathcal{P}(A \cap B) \)
Other United States Mar 12, 2025
Use the simplex method to solve the following minimum problem on your own paper. Then, using your final tableau, enter the answer in each relevant box provided below. Minimize: \( C=x_{1}+2 x_{2} \) Subject to the following constraints: \( x_{1}+x_{2} \geq 6 \) \( 2 x_{1}+4 x_{2} \geq 12 \) \( x_{1} \geq 0 \quad ; \quad x_{2} \geq 0 \) Minimum value of \( C=6 \) Value of \( x_{1}=3 \) Value of \( x_{2}=3 \)
Other United States Mar 12, 2025
The following intermediate tableau for a dual maximum problem was obtained using the simplex method for optimizing a minimum problem. \[ \left[\begin{array}{cccccc}P & y_{1} & y_{2} & s_{1} & s_{2} & R H S \\ 0 & 1 & -\frac{4}{3} & \frac{1}{3} & 0 & \frac{2}{3} \\ 0 & 0 & 1 & -\frac{1}{10} & \frac{3}{10} & \frac{2}{5} \\ \hline 1 & 0 & -10 & 2 & 0 & 4\end{array}\right] \] Perform all the necessary pivot and row operations to obtain the final tableau. Then, using the final tableau, answer the following questions: The minimum function value is: The value of \( x_{1} \) in the minimum problem is : The value of \( x_{2} \) in the minimum problem is:
Other United States Mar 12, 2025
What is the term for the remains, imprints, or traces of living things from a previous geological age? (1 point) sedimentary rocks fossils radioactive decay strata
Other United States Mar 12, 2025

Latest Other Questions

Use the simplex method to solve the following minimum problem on your own paper. Then, using your final tableau, enter the answer in each relevant box provided below. Minimize: \( C=x_{1}+2 x_{2} \) Subject to the following constraints: \( x_{1}+x_{2} \geq 6 \) \( 2 x_{1}+4 x_{2} \geq 12 \) \( x_{1} \geq 0 \quad ; \quad x_{2} \geq 0 \) Minimum value of \( C=6 \) Value of \( x_{1}=3 \) Value of \( x_{2}=3 \)
Other United States Mar 12, 2025
The following intermediate tableau for a dual maximum problem was obtained using the simplex method for optimizing a minimum problem. \[ \left[\begin{array}{cccccc}P & y_{1} & y_{2} & s_{1} & s_{2} & R H S \\ 0 & 1 & -\frac{4}{3} & \frac{1}{3} & 0 & \frac{2}{3} \\ 0 & 0 & 1 & -\frac{1}{10} & \frac{3}{10} & \frac{2}{5} \\ \hline 1 & 0 & -10 & 2 & 0 & 4\end{array}\right] \] Perform all the necessary pivot and row operations to obtain the final tableau. Then, using the final tableau, answer the following questions: The minimum function value is: The value of \( x_{1} \) in the minimum problem is : The value of \( x_{2} \) in the minimum problem is:
Other United States Mar 12, 2025
Given the following maximum problem: Maximize: \( \quad P=8 x_{1}+4 x_{2} \) Subject to the following constraints: \[ \left\{\begin{array}{l} x_{1}+x_{2} \leq 2 \\ 2 x_{1}+5 x_{2} \leq 8 \\ x_{1} \geq 0 \\ x_{2} \geq 0 \end{array}\right. \] the Initial Simplex Tableau can be formatted in this form: \[ \left[\begin{array}{cccccc} P & x_{1} & x_{2} & s_{1} & s_{2} & R H S \\ a_{11} & a_{12} & a_{13} & a_{14} & a_{15} & a_{16} \\ a_{21} & a_{22} & a_{23} & a_{24} & a_{25} & a_{26} \\ \hline & & & & & \\ a_{31} & a_{32} & a_{33} & a_{34} & a_{35} & a_{36} \end{array}\right] \] In each box below, enter the appropriate value that must replace each of the letters \( a_{11} \) through \( a_{36} \) in the above tableau.
Other United States Mar 12, 2025
Consider the following minimum problem: Minimize: \[ C=2 x_{1}+x_{2}+x_{3} \] Subject to the constraints: \[ \left\{\begin{array}{l} 2 x_{1}+x_{2}+x_{3} \geq 4 \\ x_{1}+2 x_{2}+x_{3} \geq 6 \\ x_{1} \geq 0 \\ x_{2} \geq 0 \\ x_{3} \geq 0 \end{array}\right. \] Write the dual problem for the above minimum problem by selecting the appropriate nur each blank box shown below (Do not solve the dual problem). \[ P=[\text { Select }] \quad \hat{\star} y_{1}+[\text { Select }] \quad \hat{\star} y_{2} \] [ Select ] \( y_{1}+ \) \( \square \) [ Select ] \( y_{2} \leq 2 \) [ Select ] \( y_{1}+ \) \( \square \) [Select ] \( y_{2} \leq 1 \) [ Select ] \( y_{1}+ \) \( \square \) [Select ] \( y_{2} \leq 1 \) \[ y_{1} \geq 0 \quad y_{2} \geq 0 \]
Other United States Mar 12, 2025
Use the simplex method to solve the following maximum problem: Maximize: \( \quad P=4 x_{1}+9 x_{2} \) Subject to the constraints: \( \left\{\begin{array}{l}2 x_{1}+5 x_{2} \leq 9 \\ x_{1}+2 x_{2} \leq 4 \\ x_{1} \geq 0 \\ x_{2} \geq 0\end{array}\right. \) and using your final tableau answer the questions below by entering the correct answer in each blank box. \( x_{1}=\square \) \( x_{2}=\square \)
Other United States Mar 12, 2025
Prev Next
Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy