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Source:Wikipedia:Mammoth:Mammoths are members of the family Elephantidae
Mammoths "were members of the family Elephantidae"
Parent page: Book of Mormon/Animals/Elephants
Wikipedia: Mammoths "were members of the family Elephantidae"
Mammoths could have easily been present in North America at the time of the Jaredites (the only time that elephants are mentioned in the Book of Mormon). The Wikipedia article "Mammoth" notes:
A mammoth is any species of the extinct genus Mammuthus, proboscideans commonly equipped with long, curved tusks and, in northern species, a covering of long hair. They lived from the Pliocene epoch (from around 5 million years ago) into the Holocene at about 4,500 years ago in Africa, Europe, Asia, and North America. They were members of the family Elephantidae which contains, along with mammoths, the two genera of modern elephants and their ancestors. 
- “Mammoth,” Wikipedia (accessed 24 Sept. 2014)