"No one likes anyone who does not like anyone" Which of the following are correct translations in predicate logic?

65 Views Asked by At

I am sure that there are two correct answers, i detected c but cannot detect the other.

a. $\forall x\forall y\forall z[(Person(x) \land Person(y) \land Person(z)\land \neg Likes(y,z)) \to \neg Likes(x,y)]$

b.$\forall x\forall y[(Person(x) \land Person(y)\land Likes(x,y))\to \forall z[Person(z)\to Likes(z,x)]]$

c.$\neg \exists x[Person(x) \land \forall y[Person(y)\to \neg Likes(x,y)]\land \exists z[Person(z)\land Likes(z,x)]]$

d.$\neg \exists x[Person(x) \land \exists [Person(y) \land Likes(y,x)]\land \neg \exists z[Person(z) \land \neg Likes(x,z)]]$