Yes, it is.
No. Rather all natural numbers are necessarily rational number
No. Example: The difference of 2/5 & 1/3: 2/5 - 1/3 = 1/15 ∈ ℚ (is a rational number) ∉ ℕ (is not a natural number).
Yes. The rational numbers are a closed set with respect to subtraction.
Yes, that's true.
No, it is not.
Yes. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
No, it is not true.