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sav07_homework_1_solution [2007/03/17 18:51] vkuncak |
sav07_homework_1_solution [2007/03/17 18:58] vkuncak |
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| \{(z,x) \mid \exists y. (x,y) \in r \land (y,z) \in s \} | \{(z,x) \mid \exists y. (x,y) \in r \land (y,z) \in s \} | ||
| </latex> | </latex> | ||
| + | |||
| ==== Task 4 ==== | ==== Task 4 ==== | ||
| Line 69: | Line 70: | ||
| a precondition and 2) that if we take any other precondition, it will be a subset of | a precondition and 2) that if we take any other precondition, it will be a subset of | ||
| wp. | wp. | ||
| + | |||
| + | ==== Task 5 ==== | ||
| + | |||
| + | The property | ||
| + | |||
| + | <latex> | ||
| + | wp(r,Q_1 \cup Q_2) = wp(r,Q_1) \cup wp(r,Q_2) | ||
| + | </latex> | ||
| + | |||
| + | does not hold in general. | ||
| + | |||
| + | Note: the property does hold for deterministic relations. | ||
| + | |||
| + | ==== Task 6 ==== | ||
| + | |||
| + | The property | ||
| + | |||
| + | <latex> | ||
| + | wp(r,Q_1 \cap Q_2) = wp(r,Q_1) \cap wp(r,Q_2) | ||
| + | </latex> | ||
| + | |||
| + | is true and follows from the characterization of wp in Task 4 and the distribution of the right-hand side of implication and universal quantification | ||
| + | with respect to conjunction. | ||