For Each of the Following Statements, (1) Write the Statement $\forall$

Essay

For each of the following statements, (1) write the statement informally without using variables or the symbols $\forall$ or $\exists$ , and (2) indicate whether the statement is true or false and briefly justify your answer.
(a) $\forall$ integers $a , \exists$ an integer $b$ such that $a + b = 0$ .
(b) $\exists$ an integer $a$ such that $\forall$ integers $b , a + b = 0$ .