For each of the following statements, (1) write the statement informally without using variables or the symbols ? or ?, and (2) indicate whether the statement is true or false and briefly justify your answer.

Question

(a) ? integers a, ? an integer b such that a + b = 0.
(b) ? an integer a such that ? integers b, a + b = 0.

Answer 1

a. For any integer you might choose, you can find an integer such that the sum of the two equals 0.
Or: Every integer has an additive inverse.
b. There is an integer with the property that no matter what integer is chosen, the sum of the two will be 0.
Or: Some integer has the property that its sum with every integer equals 0.