Question 22
Exactly one of the following statements is true: which one? *Please note that the numbers $a$ and $b$ need not be integers.*
A) There do not exist $a \gt 0$ and $b \gt 0$ with $a \cdot b \lt \frac{a}{b} \lt a + b$.
B) There do not exist $a \gt 0$ and $b \gt 0$ with $a \cdot b \lt a + b \lt \frac{a}{b}$.
C) There do not exist $a \gt 0$ and $b \gt 0$ with $a + b \lt a \cdot b \lt \frac{a}{b}$.
D) There do not exist $a \gt 0$ and $b \gt 0$ with $\frac{a}{b} \lt a \cdot b \lt a + b$.
E) A) through D) are false.
A) There do not exist $a \gt 0$ and $b \gt 0$ with $a \cdot b \lt \frac{a}{b} \lt a + b$.
B) There do not exist $a \gt 0$ and $b \gt 0$ with $a \cdot b \lt a + b \lt \frac{a}{b}$.
C) There do not exist $a \gt 0$ and $b \gt 0$ with $a + b \lt a \cdot b \lt \frac{a}{b}$.
D) There do not exist $a \gt 0$ and $b \gt 0$ with $\frac{a}{b} \lt a \cdot b \lt a + b$.
E) A) through D) are false.