1.Let A be a set and let ╭ A ╮ denote the set of all 2-element subsets of A
╰ 2 ╯
prove ╭ A∪B ╮ ╭ A ╮ ╭ B ╮
╰ 2 ╯ ⊇ ╰ 2 ╯ ∪ ╰ 2 ╯
╭ A∩B ╮ ╭ A ╮ ╭ B ╮
╰ 2 ╯ == ╰ 2 ╯ ∩ ╰ 2 ╯
2.Let B be a subset of A, │A│= n, │B│= k. What is the number of all subset
of A whose intersection with B has 1 element?
3.Alice has 10 balls(all different). First she splits them into two piles;
then she picks one of the piles with at least two elements, and splits it
into two; she repeats this until each pile has only one element.
Show that the number of different ways in which she can carry out this
procedure is ╭ 10 ╮.╭ 9 ╮....╭ 3 ╮.╭ 2 ╮
╰ 2 ╯ ╰ 2 ╯ ╰ 2 ╯ ╰ 2 ╯
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