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The video tutorial discusses sets as a group of elements shown within curly braces, with an empty set shown by just the curly braces or a specific symbol. Sets can be shown using the roster method by listing the elements or the set builder notation with a description for all elements. The symbol "∈" is used to refer to items that are members of a set. The tutorial also gives examples of sets with one element, multiple elements, and sets with an infinite number of elements.