Section 3.3: Problem 10 Solution

Working problems is a crucial part of learning mathematics. No one can learn... merely by poring over the definitions, theorems, and examples that are worked out in the text. One must work part of it out for oneself. To provide that opportunity is the purpose of the exercises.

James R. Munkres

Assume that $R$ is a representable relation and that $g$ and $h$ are representable functions. Show that $f$ is representable, where $f(\vec{a})=\begin{cases} g(\vec{a}) & \mbox{if }\vec{a}\in R,\\ h(\vec{a}) & \mbox{if }\vec{a}\notin R. \end{cases}$

$f$ is representable as the composition (Theorem 33L) $d(g(\vec{a}),h(\vec{a}),K_{R}(\vec{a}))$ where $g$ , $h$ , $K_{R}$ (catalog item 1), and $d(x,y,z)=x\cdot z+y\cdot(1-z)$ are representable.

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Section 3.3: Problem 10 Solution

Section 3.3: Problem 10 Solution