Converting statements with quantifiers I'm having a little trouble understanding quantifiers and therefore doubting all my study answers. Since there is no where to check if the answers are correct, I'm very very worried I am just practicing incorrectly. So I've set up two examples with what I think the answers are.
It would be brilliant if you could confirm if I am correct or not so I could use these answers as a base to check my other answers. If I am incorrect, it would be awesome if you could point me the right direction!
Example 1: Nobody except Jay and Mike is walking home.
My answer: ∀x [walking home(x) ∧ [¬ mike(x) ∧ ¬ Jay(x)]]    
Example 2: There is a time to watch, and a time to bluff; a time to fold, and a time to check. 
My answer: ∀x,y,z,v [watch(x) ∧ bluff(y) ∧ fold (z) ∧ check(v)] I chose ∀ since I've always seen it as another way of saying "always" but I could be wrong.

Example 1:  So here x is a person, walking home(x) is true if x is walking home.
∀x [walking home(x) ∧ [¬ walking home(mike) ∧ ¬ walking home(Jay)]

Example 2: Since the example says "there is a time" you should use ∃.
∃x,y,z,v [watch(x) ∧ bluff(y) ∧ fold (z) ∧ check(v)] 

