Question 99
A non-empty set $S$ of positive real numbers is called **powerful** if for any two distinct elements of it like $a$ and $b$, at least one of the numbers $a^b$ or $b^a$ is an element of $S$.
a) Present an example of a powerful set having four elements.
b) Prove that a finite powerful set cannot have more than four elements.
a) Present an example of a powerful set having four elements.
b) Prove that a finite powerful set cannot have more than four elements.