Using our logical constructions for \"exactly one\" and \"exactly two\" expressi

Question

Using our logical constructions for "exactly one" and "exactly two" expressions, convert these English sentences to logic such that their meanings are preserved. (a) Exactly one man was first on the Moon. (b) Exactly two cupcakes have chocolate frosting. As discussed in class, "exactly two" statements can be viewed as the intersection of "at most two" and "at least two." Convert these English sentences to logic such that their meanings are preserved. (a) At least two movies earned $100 million. (b) Joaquin's car can have at most two passengers.

Explanation / Answer

1)

(a) there is exactly one x man which satifies the condition first on moon P(x)

x.P(x)¬xy(P(x)P(y)xy)

(b) xy(Q(x)Q(y)xy)¬xyz(Q(x) Q(y)Q(z)xyxzy z)

2)

a) x.M(x)

b)xy(P(x)P(y)xy

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