For each of the following sentences in English, decide if the accompanying first

ID: 666477 • Letter: F

Question

For each of the following sentences in English, decide if the accompanying first-order logic sentence is a good translation.

If not, explain why no and correct it. (Some sentences may have more than one error.)

a. No two people have the same social security number

¬x,y,n Person(x) Person(y) [HasSS#(x,n) HasSS#(y,n)].

b. John's social security number is same as the Mary's

n HasSS#(John,n) HasSS#(Mary,n).

C. Everyone's social security number has nine digits.

x,n Person(x) [HasSS#(x,n) Digits(n,9)].

d. Rewrite each of the above (uncorrected) sentences using a function symbol SS# instead of the predicate HasSS#.

a) No two people have the same social security number.

The first order logic sentence is:

¬x,y,n Person(x) Person(y) [HasSS#(x,n) HasSS#(y,n)].

The given representation is incorrect because:

1) It uses the symbol with .

2) The statement also does not restrict itself in cases where the values of x and y are not equal.

Correct statement:

¬x,y,n Person(x) Person(y) ¬(x=y) (HasSS#(x,n)) HasSS#(y,n)]

b) John's social security number is same as the Mary's.

The first order logic sentence is:

n HasSS#(John,n) HasSS#(Mary,n)

This representation is correct.

c) Everyone's social security number has nine digits.

The first order logic sentence is:

x,n Person(x) [HasSS#(x,n) Digits(n,9)].

This representation is incorrect since it states that every person has a number.

Correct statement:

x,n (Person(x) HasSS#(x,n)) Digits(n,9)

¬x,y Person(x) Person(y) SS#(x)=SS#(y)

SS #(John) = SS #(Mary )

x Person(x) Digits(SS #(x ),9)

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