In each of the following, state whether the statements are true (T) or false (F).

If x and y are negative rational numbers, then so is x + y.

In each of the following, state whether the statements are true (T) or false (F).

For any rational number x, x + (–1) = –x.

In each of the following, state whether the statements are true (T) or false (F).

For rational numbers x and y, if x < y then x – y is a positive rational number.

In each of the following, state whether the statements are true (T) or false (F).

Between any two rational numbers there are exactly ten rational numbers.

In each of the following, state whether the statements are true (T) or false (F).

Rational numbers are closed under addition and multiplication but not under subtraction.