True or false

for a real number a, a + 0 = a.

for a real number a, a + (-a) = 1.

for a real numbers a and b, | a - b | = | b - a |.

for real numbers a, b, and c, a + (b ∙ c) = (a + b)(a + c).

for rational numbers a and b when b ≠ 0, is always a rational number.