Differences
This shows you the differences between two versions of the page.
Both sides previous revision Previous revision | |||
sav08:homework10 [2008/04/30 17:01] vkuncak |
sav08:homework10 [2015/04/21 17:30] (current) |
||
---|---|---|---|
Line 4: | Line 4: | ||
Let ${\cal F}$ be the set of all first-order formulas (viewed as syntax trees) and let $r$ be the implication relation on formulas: | Let ${\cal F}$ be the set of all first-order formulas (viewed as syntax trees) and let $r$ be the implication relation on formulas: | ||
- | \[ | + | \begin{equation*} |
r = \{ (F_1,F_2) \mid \models F_1 \rightarrow F_2 \} | r = \{ (F_1,F_2) \mid \models F_1 \rightarrow F_2 \} | ||
- | \] | + | \end{equation*} |
Check whether $r$ is reflexive, antisymmetric, and transitive relation. | Check whether $r$ is reflexive, antisymmetric, and transitive relation. | ||
Line 18: | Line 18: | ||
Let function $f : A \to A$ be given by | Let function $f : A \to A$ be given by | ||
- | \[ | + | \begin{equation*} |
f(x) = \left\{\begin{array}{l} | f(x) = \left\{\begin{array}{l} | ||
\frac{1}{2} + \frac{1}{4}x, \mbox{ if } x \in [0,\frac{2}{3}) \\ | \frac{1}{2} + \frac{1}{4}x, \mbox{ if } x \in [0,\frac{2}{3}) \\ | ||
Line 24: | Line 24: | ||
\frac{3}{5} + \frac{1}{5}x, \mbox{ if } x \in [\frac{2}{3},1] | \frac{3}{5} + \frac{1}{5}x, \mbox{ if } x \in [\frac{2}{3},1] | ||
\end{array}\right. | \end{array}\right. | ||
- | \] | + | \end{equation*} |
(It may help you to try to draw $f$.) | (It may help you to try to draw $f$.) | ||