Translating English statements into quantifiers and predicates. Consider the following statement: "All your friends are perfect." This can be translated into quantifiers and predicates as follows :
Let P (x) be “x is perfect” and let F (x) be “x is your friend” and let the domain be all people. So the statement can be written as : ∀x (F (x) → P (x)).
However, consider the statement: At least one of your friends is perfect. The answer is  ∃x (F (x) ∧ P (x)), but why it is not ∃x (F (x) → P (x)) ?

The last expression can be translated to English as "There is at least one person that if he is your friend then he is perfect". So there is the possibility that you don't have friends. The first expression requires you to have at least one friend. $F\land T=F$, while $F\to T=T$. Similarly, $F\land F=F$, while $F\to F=T$.
