Exercise 8.27

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. $\lnot {\exists\,x,y,n\;\;} {Person}(x) \land {Person}(y) {\:\;{\Rightarrow}\:\;}[{HasSS}\#(x,n) \land {HasSS}\#(y,n)].$

2. John’s social security number is the same as Mary’s. ${\exists\,n\;\;} {HasSS}\#({John},n) \land {HasSS}\#({Mary},n).$

3. Everyone’s social security number has nine digits. ${\forall\,x,n\;\;} {Person}(x) {\:\;{\Rightarrow}\:\;}[{HasSS}\#(x,n) \land {Digits}(n,9)].$

4. Rewrite each of the above (uncorrected) sentences using a function symbol ${SS}#$ instead of the predicate ${HasSS}#$.