Question 1

translate the given paragraphs into arguments written in F, using the given translation key. Then, derive their conclusions using the rules of inference for
-All cheetahs are faster than some tigers. Everything is striped if, and only if, it is a tiger. So, if some things are cheetahs, then some things have stripes. (Cx: x is a cheetah; Tx: x is a tiger; Sx: x has stripes; Fxy: x is faster than y)

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Question 2

translate the given paragraphs into arguments written in F, using the given translation key. Then, derive their conclusions using the rules of inference for
-All philosophers respect each other. Some philosopher doesn't study some philosopher. Anything which respects something without studying it is open-minded, if ignorant. So something is open-minded and ignorant. (Ix: x is ignorant; Ox: x is open-minded; Px: x is a philosopher; Rxy: x respects y; Sxy: x studies y)

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Question 3

determine whether the given argument is valid or invalid. If it is valid, derive the conclusion using our rules of inference and equivalence. If it is invalid, provide a counterexample.
-1. (∀x)(Ax ⊃ Dex)
2. (∃x)(Bx • Dxe)
3. (∀x)(Bx ⊃ Ax) / (∃x)[Ax • (Dxe • Dex)]

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Question 4

determine whether the given argument is valid or invalid. If it is valid, derive the conclusion using our rules of inference and equivalence. If it is invalid, provide a counterexample.
-1. (∀x)(∃y)(Pxy • ∼Pyx) 
2. (∀x)[(∃y)Pxy ⊃ (∃y)Qxy] / (∀x)(∃y)(Qxy • ∼Pyx)

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Question 5

determine whether the given argument is valid or invalid. If it is valid, derive the conclusion using our rules of inference and equivalence. If it is invalid, provide a counterexample.
-1. (?x)[Tx ? (?y)(Sy • Wxy)]
2. (?x)(Sx • Vx)
3. (?x)(Tx • Rx) / (?x)[(Rx • Vx) • (?y)Wxy]

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Question 6

determine whether the given argument is valid or invalid. If it is valid, derive the conclusion using our rules of inference and equivalence. If it is invalid, provide a counterexample.
-1. (?x)[Lx ? (?y)(My • Nxy)]
2. (?x)[Lx • (?y)Nxy] / (?x)[Mx • (?y)Nxy]

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Question 7

use:
d: Diego 
s: Sean
Dx: x is on the Dean's list 
Px: x is a philosophy major 
Sx: x is a student
Vx: x is a valedictorian
-There is exactly one philosophy major on the Dean's list.

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