Exercise 1.6.6

Question

%1.6.6
  \begin{enumerate}[label=(\alph*)] 
  \item Using the particular set $A=\{a, b, c\}$, exhibit two different $1-1$ mappings from $A$ into $P(A)$.
  \item Letting $C=\{1,2,3,4\}$, produce an example of a $1-1$ map $g: C \rightarrow P(C)$.
  \item Explain why, in parts (a) and (b), it is impossible to construct mappings that are onto.
   \end{enumerate}

Ulisse Mini · Accepted Answer

\begin{enumerate}[label=(\alph*)] 
  \item $f(x) = \{x\}$, $f(x) = \{x, b\}$ for $x 
e b$ and $f(x) = \{a,b,c\}$ for $x=b$.
  \item $f(x) = \{x\}$.
  \item We can hit at most $n$ elements in the power set out of the $2^n$ total elements.
   \end{enumerate}

Exercise 1.6.6

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Exercise 1.6.6

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