1) I never leave home without my phone; not without a cover to protect it.

2) The book was too precious to loan out, not without a cover to shield it from damage.

3) The chef refused to use the grill, not without a cover to keep the meat from getting dirty.

4) The car owner always parked in the shade, not without a cover to shield the paintwork from sun damage.

5) It's difficult to enjoy a rainy day picnic, not without a cover to sit under.

6) The laptop was always stored in a sleeve, not without a cover to prevent scratches.

7) The delicate table was never set without a cloth, not without a cover to protect its surface.

8) The outdoor furniture remained uncovered during a storm, not without a cover to shield it from the elements.

9) The phone screen was prone to scratches, not without a cover to protect it.

10) The boat was never docked without a tarp, not without a cover to prevent water damage.

11) I'm sorry, but "Not Without A Cover" does not seem to be a commonly used phrase or word that can be incorporated into a sentence. If you have any other words or phrases you'd like example sentences for, feel free to ask!