Problem 144 (difficulty: 5/10)

Let \(\displaystyle H,K\) be non-empty subsets of the real line \(\displaystyle \R\). What is the logical connection between the following two statements?

a) \(\displaystyle \sup H < \inf K\);

b) \(\displaystyle \forall x\in H\) \(\displaystyle \exists y\in K\) \(\displaystyle x<y\).

Give me another random problem!