Q1: Let $(G, \circ)$ be a group and $H \subseteq G$ be a subset. What does $H \leq G$ mean?

A1: $H$ together with the binary operation $\circ$ forms a group.

A2: $H$ is empty.

A3: The neutral element of $(G, \circ)$ is not an element of $H$.

A4: $H$ is biggest subgroup of $G$.

Q2: Let $(G, \circ)$ be a group and $H \subseteq G$ be a non-empty subset. What is equivalent to $H \leq G$?

A1: $a \circ b \in H$ and $a^{-1} \in H$ for every $a,b \in H$.

A2: $a \circ b \in H$ and $a \in H$ for every $a,b \in H$.

A3: $a \circ b \in H$ and $a^{-1} \in H$ for every $a,b \in G$.

A4: $a \circ b^{-1} \in H$ for every $a,b \in G$.

Q3: Let $(G, \circ)$ be a group with four elements. What is always correct?

A1: $G$ is an abelian group.

A2: $G$ is the Klein four group.

A3: $G$ is $\mathbb{Z}/4\mathbb{Z}$

A4: $G$ has 3 subgroups.