For each of the following sentences in English, decide if the
accompanying first-order logic sentence is a good translation. If not,
explain why not and correct it. (Some sentences may have more than one
error!)
1. No two people have the same social security number. ¬∃x,y,nPerson(x)∧Person(y)⇒[HasSS#(x,n)∧HasSS#(y,n)].
2. John’s social security number is the same as Mary’s. ∃nHasSS#(John,n)∧HasSS#(Mary,n).
3. Everyone’s social security number has nine digits.
∀x,nPerson(x)⇒[HasSS#(x,n)∧Digits(n,9)].
4. Rewrite each of the above (uncorrected) sentences using a function symbol SS# instead of the predicate HasSS#.
1. No two people have the same social security number. ¬∃x,y,nPerson(x)∧Person(y)⇒[HasSS#(x,n)∧HasSS#(y,n)].
2. John’s social security number is the same as Mary’s. ∃nHasSS#(John,n)∧HasSS#(Mary,n).
3. Everyone’s social security number has nine digits.
∀x,nPerson(x)⇒[HasSS#(x,n)∧Digits(n,9)].
4. Rewrite each of the above (uncorrected) sentences using a function symbol SS# instead of the predicate HasSS#.
For each of the following sentences in English, decide if the
accompanying first-order logic sentence is a good translation. If not,
explain why not and correct it. (Some sentences may have more than one
error!)
1. No two people have the same social security number.
¬∃x,y,nPerson(x)∧Person(y)⇒[HasSS#(x,n)∧HasSS#(y,n)].
2. John’s social security number is the same as Mary’s.
∃nHasSS#(John,n)∧HasSS#(Mary,n).
3. Everyone’s social security number has nine digits.
∀x,nPerson(x)⇒[HasSS#(x,n)∧Digits(n,9)].
4. Rewrite each of the above (uncorrected) sentences using a function
symbol SS# instead of the predicate HasSS#.