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.
1. Any apartment in London has lower rent than some apartments in Paris.
$$\forall {x} [{Apt}(x) \land {In}(x,{London})] \implies \exists {y} ([{Apt}(y) \land {In}(y,{Paris})] \implies ({Rent}(x) < {Rent}(y)))$$ 2. There is exactly one apartment in Paris with rent below \$1000. $$\exists {x} {Apt}(x) \land {In}(x,{Paris}) \land \forall{y} [{Apt}(y) \land {In}(y,{Paris}) \land ({Rent}(y) < {Dollars}(1000))] \implies (y = x)$$ 3. If an apartment is more expensive than all apartments in London, it must be in Moscow. $$\forall{x} {Apt}(x) \land [\forall{y} {Apt}(y) \land {In}(y,{London}) \land ({Rent}(x) > {Rent}(y))] \implies {In}(x,{Moscow}).$$ 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. 1. Any apartment in London has lower rent than some apartments in Paris. $$\forall {x} [{Apt}(x) \land {In}(x,{London})] \implies \exists {y} ([{Apt}(y) \land {In}(y,{Paris})] \implies ({Rent}(x) < {Rent}(y)))$$ 2. There is exactly one apartment in Paris with rent below \$1000.
$$\exists {x} {Apt}(x) \land {In}(x,{Paris}) \land \forall{y} [{Apt}(y) \land {In}(y,{Paris}) \land ({Rent}(y) < {Dollars}(1000))] \implies (y = x)$$ 3. If an apartment is more expensive than all apartments in London, it must be in Moscow.
$$\forall{x} {Apt}(x) \land [\forall{y} {Apt}(y) \land {In}(y,{London}) \land ({Rent}(x) > {Rent}(y))] \implies {In}(x,{Moscow}).$$

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