Question

Indicate whether the following statements are True (T) or False (F). You must get all answers correct in order to receive credit.

1. The difference of two integers is always a natural number.
2. The difference of two integers is always an integer.
3. The sum of two integers is always an integer.
4. The quotient of two integers is always an integer (provided the denominator is non-zero).
5. The ratio of two integers is always positive
6. The product of two integers is always an integer.
7. The quotient of two integers is always a rational number (provided the denominator is non-zero).

Answer 1

1: F - since 0 can be the result of a difference, and it is not natural(ie 1,2,3....)
2: T - since 0 and any negatives(assuming no preference in magnitude) are integers
3: T - Same as above
4: F - since integers are not ration, but you can have fractions(ie rationals)
5: F - since the ratio can be negative if one but not the other is negative
6: T - since you cannot have a fraction(ie rational) based on solely integers
7: T - Since Rational Numbers encompass integers(ie Rationals are a superset)