Recall the definition of injective and surjective functions:
1.a A function $f: X \to Y$, is injective if for all $a,b \in X$, if $a \neq b$, then $f(a) \neq f(b)$
1.b A function $f: X \to Y$, is injective if for all $a,b \in X$, if $f(a) = f(b)$, then $a = b$
- A function $f: X \to Y$, is surjective if for all $y \in Y$, $\exists x \in X$, such that $f(x) =y$
I would like to extend them into sets, I don't know if these extensions are correct.
1.a A function $f: X \to Y$, is injective if for all $A, B \subseteq X$, if $A \cap B = \varnothing$, then $f(A) \cap f(B) = \varnothing$
1.b A function $f: X \to Y$, is injective if for all $A, B \subseteq X$, if $f(A) = f(B)$, then $A = B$
- A function $f: X \to Y$, is surjective if for all $B \subseteq Y$, $\exists A \subseteq X$, such that $f(A) = B$
Can someone please check if these "set extensions" are correct?
Per Brian's suggestion I have edited 1.b