Answer:
A is always true, B is false, C is always true, D is sometimes true, E is always true, F is always true, G is always true, H is sometimes true.
Step-by-step explanation:
A: Anything greater than (>) 0 is positive. X is greater than zero.
B: X < 0 is false because X CANNOT be less than 0. It is a positive integer, meaning it has to be greater than 0.
C: X has to be greater than 0, so it has to be greater than -5 since -5 is less than 0.
D: 1 is a positive integer. We don't know what specific integer X represents. It could be 1, it could be greater than 1. It's sometimes true.
E: Any integer greater than or equal to 1 (≥) is a positive integer. X is a positive integer, so this is always true.
F: 0 is not a positive integer, so X cannot equal 0 (≠).
G: X has to be greater than 0 to be a positive integer, so it cannot equal -1 (≠) since -1 is less than 0.
H: The specific value of X is not stated, so it could be 5, it could be another positive integer. This is sometimes true.