It is possible, but of course this depends on the size, age and sex of the moose and the bear, and the species of the bear. A bull moose has strong, large antlers and long sharp hooves (cows only have their hooves to defend themselves with) that could do serious damage to the bear. Most bears, no matter the species, won't mess with an animal that can fight back, especially a moose. However, a bear like a large grizzly or Alaskan brown bear might be able to injure a moose if it was really angry, or large and fearless enough to put up a good fight against such a raging herbivore. A bear would have to claw and bite it's way out of a fight with a moose, but Lord help them if that moose is an angry bull on the rut with those powerful antlers. But as far as a moose being able to kill a bear, such cases may be rare because often either party would wish to run away to save themselves rather than getting killed.
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Possibly. Those sharp hooves can deliver quite the lacerations to a marauding and threatening predator like a bear, and some lacerations may be enough to kill, especially if they strike a large vein or artery that would make a bear bleed to death. However, cow moose don't go out of their way to actively kill black bears, they only do so by chance because the only thing on their minds is to either defend their calves or to get the threat out of the area as soon and fast as possible by any means. Cow moose are very dangerous when protecting their calves from any predator, including black bears.
It's not likely that a cow moose is able to kill a grizzly bear. She would do more injury to a bear than kill it, more from the slashes with her hooves than anything else. She won't be using her head or anything else, just her hooves to strike out with. Since moose are herbivores and prey animals, they would rather take flight over fight, and if cornered do anything they can to get away or defend itself against a large imposing predator like a grizzly bear.
In the act to defend herself, either in a very fearful or panicked (or both) state, a cow moose, however, may kill a grizzly with her hooves, but it's never on purpose. Most moose (except bulls during rutting season) will not go about its business to actively kill other animals. The most likely way that a cow moose could kill a grizzly is if her hooves catches the bear in the neck and severs the jugular vein with her sharp hooves. A bear would die from its injuries if she broke its jaw or nose, making it very painful for it to eat. If a bear can't eat, it starves to death.
A brown bear could kill a cow moose, but not really a bull moose.
If a large brown bear happened to attack a bull moose on the rut, the large brown bear would get itself mauled by the rutting bull moose. The large brown bear would be able to injure a rutting bull moose if it was very angry.
Yes, a bull moose could kill a grizzly bear. Bull moose on rut can kill anything that gets in its way, even a grizzly bear that is about to attack it in a manner than is very devastating. They have huge antlers that are sharper than daggers, and can be big enough to kill a grizzly bear in a single hit or two. Rutting bull moose have powerful hooves, a weight advantage, and those two huge antlers that are very strong, with an aggression in fight down attacking predators. Bull moose can stand a chance against a grizzly bear as long as the bull moose is on the rut, and is about to attack the grizzly bear. However, a grizzly bear is strong enough to injure a bull moose on the head by swiping its head with those large claws/teeth and a adequate weight strength of attacking. The bull moose would already hit the grizzly bear with its antlers, before the grizzly bear attempted to grab on the bull moose's head side to bite its throat. A bull moose can kill a black bear, a grizzly bear, a brown bear, but not really a polar bear.
No. A black bear may try to kill a moose calf if it wondered off by itself, but it would never dare to take on and kill a full grown adult, unless it is too weak or wounded to defend itself.
Yes. A grizzly bear or a brown bear can even kill and eat an adult bull moose alone, only if the bull moose is not on the rut.