Let $(G_1,\circ_1)$ be a group with composition law $\circ_1$ and $(G_2,\circ_2)$ a group with composition law $\circ_2$.
Let $f:G_1\rightarrow G_2$ be a group homomorphism.
The group homomorphism $f$ is defined to be injective if and only if, for $g_1, g_1'\in G_1$:
$f(g_1)=f(g_1')$ implies $g_1=g_1'$
...a synonym for "injective homomorphism" is "monomorphism", and we also say "the homomorphism is one-to-one".
Which of the following are true? Select ALL that apply.