I am having a (rather standard) daily maintenance plan created with SQL Server Management Studio Maintenance Plan Wizard.

AFAIU, the penultimate task "Back Up Database Task" will be executed only on the success of all preceding tasks. Since the constraints (arrows containing tasks) are all the same (taken from default options creation):

and use "Logical AND"
Now if I change in the preceding constraint the "Logical AND" to "Logical OR", the backup task still will fail if one of the preceding tasks fail.
Correct?
How can I make the backup task to run in any case?
UPDATE
After accepting the answers, I am still in doubt about the term "completion":
Does failed task considered to be run to completion in SQL Server maintenance plan terminology?
