Let $S = \{3,B\}$
Give an example of a function $f: S \times S \to S$ that is onto.
Give an example of a function $g: S \to S \times S$ that is 1-1.
Give an example of a function $h: P(S) \to S \times S$ that is 1-1 and onto.
Trying to revise for exam, but simply cannot understand 1-1 and onto functions.
Thanks for any guidance.
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$\begingroup$One-to-one functions (often called injective function) map each element from its domain to distinct values in its codomain. That is, if you have a one-to-one function $f\colon A\rightarrow B$ and two distinct values $x,y\in A$, you know that $f(x)\neq f(y)$.
Onto functions (often called surjective functions) "fill" the entire codomain in the sense that if you take $b\in B$ and $f\colon A\rightarrow B$ is onto, you know that there exist a $a\in A$, such that $f(a)=b$.
As an example, in your first assigment, you could choose the function$f\colon S\times S\rightarrow S$, that maps $(a,b)\in S$ to $a\in S$.
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