So this is a question From a Script. It didnt work out for me for more than 3 hours now. First i thought its the Option a) there is one guy in every City With a car but then i Decides that its more likely b) in every City there is a guy With no car. I really cant write it right With quantifiers and i would be more than happy if someone here could help me. Hopefully, reegards! Also if someone could send a link to similar questions i would be very happy!
2026-03-26 07:59:06.1774511946
On
On
what is equivalent to "in no city there is no guy with no car"?
53 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
3
There are 3 best solutions below
5
On
"in no city, there is no guy with no car" = "in no city, every guy has a car" = "there is no city where every guy has a car" = "in every city there is at least one guy does not have a car".
0
On
$$\neg \exists x (City(x) \land \neg \exists y (Guy(y) \land In(y,x) \land \neg \exists z (Car(z) \land Has(y,z)))) \Leftrightarrow$$
$$\forall x (City(x) \rightarrow \neg \neg \exists y (Guy(y) \land In(y,x) \land \neg \exists z (Car(z) \land Has(y,z)))) \Leftrightarrow$$
$$\forall x (City(x) \rightarrow \exists y (Guy(y) \land In(y,x) \land \neg \exists z (Car(z) \land Has(y,z)))) \Leftrightarrow$$
$$\forall x (City(x) \rightarrow \exists y (Guy(y) \land In(y,x) \land \forall z (Car(z) \rightarrow \neg Has(y,z))))$$
So:
In every city lives a guy that does not have a car
Start with "no guy with no car", that means "there does not exist a guy that has zero cars" and you can then cancel the two negatives (which I assume you already know how) to "all guys have at least one car" and you can keep going.