Explanation:
{x : x < 100}
means all numbers smaller than 100. but that includes all negative numbers. so, NO.
y
while this includes all positive numbers, it also includes all numbers between -0.1 and 0. e.g. -0.001
so, NO
x in N
N is the set of all natural numbers. that is the set of all positive integers.
so, YES
{y : 0 < y < 1}
that is all numbers between 0 and 1. that's are only positive numbers between 0 and 1.
so, YES
x in Z
Z is the set of all integer numbers (including the negative ones). so, NO
{y : 3 <= y < 22}
ask numbers between 3 and 22, including 3. there are only positive numbers, as there cannot be suddenly a negative number between 2 positive numbers.
so, YES.