Translate the following argument into propositional logic using the translation key provided:”If the economy grows, then unemployment will decrease. If unemployment decreases, then consumer spending will rise. Therefore, if the economy grows, then consumer spending will rise.”Translation Key:G: The economy growsU: Unemployment will decreaseC: Consumer spending will rise

Is the following sentence a tautology? Show your work with a truth table.(P→(Q→P))

Identify the error in the following reasoning:1. (P→Q)        Premise2. (Q→R)        Premise  |_________3. | P         Assumption for CD4. | Q         MP, 1, 35. | R         MP, 2, 46. (P→R)        CD, 3-57. Q            MP, 1, 3 

Once a conditional derivation subproof is complete, which of the following is TRUE?

Complete this conditional derivation proof: Premises: (A→B), (B→C) Conclusion: (A→C) 1. (A→B)        Premise 2. (B→C)        Premise   |_________ 3. | A         Assumption for CD 4. | _[BLANK-1]_     MP, 1, 3 5. | _[BLANK-2]_     MP, 2, 4 6. (A→C)        CD, 3-5 Fill in lines 4 and 5.

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Answer the question based on what you see in the drawing (not what you imagine is in the drawing) Estudiante A:  ¿Dónde están las mochilas? Estudiante B:  Las mochilas están __________ de la mesa.

Fill in the blank with the present-tense form of the verb provided in parentheses.  (comprender)     Mi hermanito  __________ que es muy importante leer libros. 

Fill in the blank with the present-tense form of the verb provided in parentheses.    (preferir) Tú ______________________ (preferir) nadar en la piscina.   

Write a description of your favorite friend or family member. Include his/her everyday activities and favorite sports or pastimes. Use vocabulary from textbook Lessons 1–4. Write at least 5 complete sentences. (6 pts. for vocabulary + 6 pts. for grammar + 3 pts. for style = 15 pts.)