Using the predicate symbols shown and appropriate quantifiers, write each Englis

Question

Using the predicate symbols shown and appropriate quantifiers, write each English language statement as
a predicate wff. (The domain is the whole world.)
C(x): x is a Corvette
F(x): x is a Ferrari
P(x): x is a Porsche
S(x, y): x is slower than y
a. Nothing is both a Corvette and a Ferrari.
b. Some Porsches are slower than only Ferraris.
c. Only Corvettes are slower than Porsches.
d. All Ferraris are slower than some Corvettes.
e. Some Porsches are slower than no Corvette.
f. If there is a Corvette that is slower than a Ferrari, then all Corvettes are slower than all Ferraris.

Explanation / Answer

a. Nothing is both a Corvette and a Ferrari.

Ans: C(x) ^ F(x) means Corvette and a Ferrari.

? ( ? x)( C( x) ? F( x))

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b. Some Porsches are slower than only Ferraris.

Ans:

( ? x)( P(x) ? ? ( ?y)( S( x, y) ? F( y)))

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c. Only Corvettes are slower than Porsches.

Ans:

?x)( ?y)(( P( y) ? S( x, y)) ? C( x))
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d. All Ferraris are slower than some Corvettes.

Ans:

( ?x)( F( x) ? ( ? y)( C( y) ? S( x, y)))

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e. Some Porsches are slower than no Corvette.

Ans:

( ? x)( P( x) ? ( ?y)( C( y) ?? S( x, y)))

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f. If there is a Corvette that is slower than a Ferrari, then all Corvettes are slower than all Ferraris.

Ans:

( ? w)( ? x)( C( w) ? F( x) ? S( w , x)) ? ( ?y)( ?z)(( C( y) ? F( z)) ? S( y , z))

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