For each task, you can choose to treat the input link as an AND link or an OR link. When a task has one input link, the Integration Service processes the task when the previous object completes and the link condition evaluates to True. If you have multiple links going into one task, you can choose to have an AND input link so that the Integration Service runs the task when all the link conditions evaluates to True. Or, you can choose to have an OR input link so that the Integration Service runs the task as soon as any link condition evaluates to True.
To set the type of input links, double-click the task to open the Edit Tasks dialog box. Select AND or OR for the input link type.