Rumer Willis sunglasses demi morre shopping jeans gun purse gun bag

A somber-looking Rumer Willis went to the Beverly Glen mall in Brentwood on Monday, and later we spotted the Sorority Row starlet grabbing some dog food at a pet store in Los Angeles. But what caught our eye was her handgun handbag! Talk about packing heat.

When asked about Demi Moore's hospitalization, Rumer refused to comment, and it appears as though her mother's troubles have affected her as well -- it seems like she's lost a few pounds, and she definitely doesn't look like she's been sleeping well.

As you know, Demi was rushed to the hospital last weekend after smoking a mysterious substance and going into convulsions, so we're glad to see that Rumer is able to handle her business. Hopefully her mother is getting the rest and help she needs...