### Artificial IntelligenceAIMA Exercises

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 ${HasSS}\#$.

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 ${HasSS}\#$.

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