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sav08:relations [2008/02/21 20:14] piskac |
sav08:relations [2008/02/21 22:42] piskac |
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| + | ===== Relations ===== | ||
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| __Exercise:__ | __Exercise:__ | ||
| Prove that it holds or construct a counterexample which shows that it does not hold: | Prove that it holds or construct a counterexample which shows that it does not hold: | ||
| * <latex>r \circ (s \cap t) \subseteq (r \circ s) \cap (r \circ t)</latex> | * <latex>r \circ (s \cap t) \subseteq (r \circ s) \cap (r \circ t)</latex> | ||
| - | - <latex>(r \circ s) \cap (r \circ t) \subseteq r \circ (s \cap t)</latex> | + | * <latex>(r \circ s) \cap (r \circ t) \subseteq r \circ (s \cap t)</latex> |
| - | - <latex>(r \circ s)^{-1} = s^{-1} \circ r^{-1}</latex> | + | * <latex>(r \circ s)^{-1} = s^{-1} \circ r^{-1}</latex> |
| __Solution:__ | __Solution:__ | ||
| - | aaaa | + | Solutions can be found [[http://lara.epfl.ch/dokuwiki/doku.php?id=sav07_homework_1_solution|in the material from the last year]] (Task 1, 2 and 3) |