Help with order of quantifiers

Question

I have to say if the following are true or false and why. Can someone check to see if I understand how orders of quantifiers affect the meaning?

1. For every integer x, there exists an integer y such that y>x. True. Whatever integer x is, there will be a bigger y.
2. There exists an integer x such that for every integer y, y>x. False. If x is a specific integer, there's a possibility that a y is smaller.
3. For every integer x and y, y>x. False. There's a possibility that the x>y.
4. There exists an x and y such that y>x.
   True. It is possible that for one chosen x, there is a y that is larger.

Thank you!