Problem 138 (difficulty: 2/10)

Let \(\displaystyle H\) be a subset of the reals. Which properties of \(\displaystyle H\) are expressed by the following formulas?
 (1)  \(\displaystyle (\forall x\in \R) (\exists y\in H) (x<y);\)
 (2)  \(\displaystyle (\forall x\in H) (\exists y\in \R) (x<y);\)
 (3)  \(\displaystyle (\forall x\in H) (\exists y\in H) (x<y).\)

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