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sav08:sets_and_relations [2009/03/10 20:29] vkuncak |
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| Generalization of function update is override of partial functions, $f \oplus g$ | Generalization of function update is override of partial functions, $f \oplus g$ | ||
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| ==== Range, Image, and Composition ==== | ==== Range, Image, and Composition ==== | ||
| + | The following properties follow from the definitions: | ||
| \[ | \[ | ||
| - | S \bullet r = ran(\Delta_S \circ r) | + | (S \bullet r_1) \bullet r_2 = S \bullet (r_1 \circ r_2) |
| \] | \] | ||
| \[ | \[ | ||
| - | (S \bullet r_1) \bullet r_2 = S \bullet (r_1 \circ r_2) | + | S \bullet r = ran(\Delta_S \circ r) |
| \] | \] | ||
| Line 309: | Line 311: | ||
| * [[:Gallier Logic Book]], Chapter 2 | * [[:Gallier Logic Book]], Chapter 2 | ||
| + | * [[sav08:discrete_mathematics_by_rosen|Discrete Mathematics by Rosen]] | ||