question.md

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 ${HasSS}#$.