Practice Exam #4

 

General Instructions: This exam has six parts. Be sure to complete each part. Read the instructions completely before attempting to answer specific questions. All answers go in a blue book with your name on it.

 

Part I Translation (4 points each, 20 points total)

 

1.Everyone who is taller than Ignat is shorter than Tony.

 

2.There is someone who likes everyone.

 

3. No hard-drinking Texans knit.

 

4. No film critic loves every movie.

 

5. Some dark chocolate is neither sweet nor high in carbohydrates.

 

Part II Translation with Identity (5 points each, 10 points total)

 

1. There are exactly two fish.

 

2. Bertha is the tallest philosopher.

 

Part III Testing for Validity Using the Model Universe Method (10 points total)

 

1. (x)(Sx ⊃ Tx), (∃x)Tx, // (∃x)Sx

 

Part IV Testing for Validity Using the Truth-Tree Method (10 points each, 20 points total)

 

1. (∃x)(Ax & ~Bx), (x)(Bx ⊃ ~Cx) // (x)(Cx ⊃ ~Ax)

 

3. (x)(y)(Rxy ⊃ ~Txy), (∃x)( y)(Txy & ~ Uxy) // (∃x)(∃y)(Rxy ⊃ Uxy)

Part V Proofs (15 points each; 30 points total.)

 

1.     (x)(~Ax ⊃ Kx), (∃x)~Kx /// (∃x)(Ax v ~Bx)

 

2.     /// (x)Fxa ⊃ (x)(∃y)Fxy

 

Part VI Essay (10 points)

 

Can you determine whether (∃x)(y)~Txy is logically true? Explain.

 

** Practice Exam Solutions **