The set is not closed
Example:
-4 * -3 = 12 this is not a negative integer
Answer:
x²-8x-1=0
comparing above equation with ax²+bx+c=0
a=1
b=-8
c=-1
x=

=(--8+-√(64-4×1×-1)/2×1
=8+-√(64+4)/2
taking positive
x=(8+√68)/2=2(4+√17)/2=4+√17
taking negative
x=(8-√68)/2=2(4-√17)/2=4-√17
This argument is no valid although the first part of the statement is valid. If a number is larger than 6 than its square must be larger than 36. But if the number is smaller than 6, its square does not need to be smaller than 36. For example...
(-100)²=10000
-100 is smaller than 6 but its square is bigger.
answer: False