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

question 8

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 $b , a + b = 0$ .

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Definitions:

Stairs

A series of steps constructed for the purpose of providing access between different floors or levels.

Iron-Eating Bacteria

Microorganisms that derive their energy by oxidizing ferrous iron compounds, leading to the corrosion of iron-based materials.

Basketball Player

An athlete who participates in basketball, a team sport involving shooting a ball through an opponent's hoop to score points.

Juicy

Juicy refers to something that is full of juice or moisture, often used to describe flavorful and succulent fruits or stories that are especially interesting and scandalous.