Problem 146 (difficulty: 5/10)

Let \(\displaystyle A,B\) be subsets of the real line \(\displaystyle \R\) such that \(\displaystyle A\cup B=(0,1)\). Does it imply that

\(\displaystyle \inf A=0\qquad\hbox{or}\qquad \inf B=0\qquad?\)

Give me another random problem!