Mike always loves ships. When he was older, he said, “I'm going to be a soldier.” But his eyes were not very1and he did not get in.

    Then he said, “I'm going to2a small boat and I'm going around the world.” But boats were very expensive, and Mike did not have enough3

    Last summer Mike found a swimming4near his house. The lessons did not cost very5 and Mike began going to the school at every end of the week and having6. Now he is a good swimmer.

    Last week a little boy said to him, “You're a very good swimmer. How do7learn to swim so well?”

    “I'm not good at all,” Mike said and he smiled. “8 I'm in the water, I say to myself, “There are 9fishes behind me!” Then I'm very afraid, and I10quickly.”

设集合S_n={1，2，3…n}，若X是S_n的子集，把X中所有元素的和称为X的“容量”（规定空集的容量为0），若X的容量为奇（偶）数，则称X为S_n的奇（偶）子集．

（Ⅰ） 写出S₄的所有奇子集；

（Ⅱ） 求证：S_n的奇子集与偶子集个数相等；

（Ⅲ）求证：当n≥3时，S_n的所有奇子集的容量之和等于所有偶子集的容量之和．