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

Question

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 $x , x < y$.

Quizplus · Accepted Answer

The Answer is a. Given any real number, there is a real number that is less than the given number.
Or: There is no smallest real number.
b. There is a real number that is less than every real number.

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

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