Say A is empty.
Could I do A --> B (1-1) or B --> A (1-1)?
Thanks.
Every mapping $\displaystyle f:\varnothing\mapsto X$ is injective. To see this merely note that for the condition that there exists $\displaystyle x_1,x_2\in\text{Dom}(f)$ such that $\displaystyle f(x_1)=f(x_2)$ we would have to say $\displaystyle x_1,x_2\in\varnothing$. See a problem?
For $\displaystyle f:X\mapsto\varnothing$ it actually reverts to the same thing. For suppose that $\displaystyle X\ne\varnothing$ then for any $\displaystyle x\in X$ we would have that $\displaystyle f(x)$ does not exist? Why? Thus, if $\displaystyle f:X\mapsto\varnothing$ and $\displaystyle f$ is well-defined then by necessity we must have that $\displaystyle X=\varnothing$.