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

question 4

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) $\forall$ real numbers $x , \exists$ a real number $y$ such that $x < y$ .
(b) $\exists$ a real number $y$ such that $\forall$ real numbers $x , x < y$ .

---

Definitions:

Perpetual Scholarship

A scholarship grant maintained indefinitely, often funded by an endowment that generates interest to cover its cost.

Compounded Annually

An interest calculation method where the interest is added to the principal at the end of each year, with the total becoming the principal for the next year.

Compounded Annually

A method where interest is calculated once per year and added to the principal sum.

Withdrawals

The act of removing funds from a bank or investment account.