Introduction to groups

Select all groups from the list of pairs (set, binary operation).

Everywhere, if the opposite isn't told explicitly, $+$ and $\cdot$ denote the ordinary addition and multiplication. $\mathbb{R}$ is the set of real numbers, $\mathbb{R}^{*} = \mathbb{R} \setminus \{0\}$. $\mathbb{Q}$ is the set of rational numbers, $\mathbb{Q}^{*} = \mathbb{Q} \setminus \{0\}$.