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Where and what is "Lybia"?

If you mean Libya, that is a NATO action, and there seem to be no active U.S. participants. You have perhaps heard of the North Atlantic Treaty Organization?

There have been no U.S. military casualties because there is no U.S. military participation in the field.

U.S. efforts have been primarily moral and diplomatic.

The British, French, and others of the many nations involved have been quite active.

Perhaps it has escaped your notice, but the United States is reducing its combat commitments.