SOme logic problems to be solved asap..plzzz help

Prove/Disprove following preposition.

1. x, y are real numbers greater than zero., for every x there is a y, then
x^2 + y^2 greater or equal to zero.

2. x, y are real numbers greater than zero.,for all y there is some x, then
x^2+ y^2 greater or equal to zero.

3. x, y are real numbers greater than zero, for every x there is a y, then
if x<y then (x^2) <(y^2)

4. x, y are real numbers greater than zero.,for all x there is some y, then
if x<y then (x^2) <(y^2)

5. x, y are real numbers, for some x there is some y, then
if x<y then (x^2) <(y^2)

6. Let m; n be natural numbers, m, n are even ,then (m + n) is also even
7. Let m; n be natural numbers, (m is even ^ n is odd) )then (m + n) is even
8. all x are whole numbers, then n^2 greater than equal to 2^n