分别写出集合{a1},{a1,a2,a3},{a1,a2,a3,a4}的子集.由此猜想集合{a1,a2,a3 .an}的子集的个数
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![分别写出集合{a1},{a1,a2,a3},{a1,a2,a3,a4}的子集.由此猜想集合{a1,a2,a3 .an}的子集的个数](/uploads/image/z/6818493-21-3.jpg?t=%E5%88%86%E5%88%AB%E5%86%99%E5%87%BA%E9%9B%86%E5%90%88%7Ba1%7D%2C%7Ba1%2Ca2%2Ca3%7D%2C%7Ba1%2Ca2%2Ca3%2Ca4%7D%E7%9A%84%E5%AD%90%E9%9B%86.%E7%94%B1%E6%AD%A4%E7%8C%9C%E6%83%B3%E9%9B%86%E5%90%88%7Ba1%2Ca2%2Ca3+.an%7D%E7%9A%84%E5%AD%90%E9%9B%86%E7%9A%84%E4%B8%AA%E6%95%B0)
分别写出集合{a1},{a1,a2,a3},{a1,a2,a3,a4}的子集.由此猜想集合{a1,a2,a3 .an}的子集的个数
分别写出集合{a1},{a1,a2,a3},{a1,a2,a3,a4}的子集.由此猜想集合{a1,a2,a3 .an}的子集的个数
分别写出集合{a1},{a1,a2,a3},{a1,a2,a3,a4}的子集.由此猜想集合{a1,a2,a3 .an}的子集的个数
{a1}的子集:φ,{a1}【2个=2^1】
{a1,a2,a3}的子集:φ,{a1},{a2},{a3},{a1,a2},{a1,a3},{a2,a3},{a1,a2,a3}【8个=2^3】
{a1,a2,a3,a4}的子集:φ,{a1},{a2},{a3},{a4},{a1,a2},{a1,a3},{a1,a4},{a2,a3},{a2,a4},{a3,a4},{a1,a2,a3},{a1,a2,a4},{a1,a3,a4},{a2,a3,a4},{a1,a2,a3,a4}【16个=2^4】
故猜想集合{a1,a2,a3 .an}的子集的个数为2^n个
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2的N次方
{a1}子集:空集.{a1}共2个子集
{a1,a2,a3}子集:空集,.{a1}.{a2}.{a3}.{a1,a2}.{a1,a3}.{a2,a3}.{a1,a2,a3}共8个子集
{a1,a2,a3,a4}的子集:空集,.{a1}.{a2}.{a3}.{a4}.{a1,a2}.{a1,a3}.{a1,a4}.{a2,a3}.{a2,a4}.{a3,a4}.{a1,a2,a3}....
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{a1}子集:空集.{a1}共2个子集
{a1,a2,a3}子集:空集,.{a1}.{a2}.{a3}.{a1,a2}.{a1,a3}.{a2,a3}.{a1,a2,a3}共8个子集
{a1,a2,a3,a4}的子集:空集,.{a1}.{a2}.{a3}.{a4}.{a1,a2}.{a1,a3}.{a1,a4}.{a2,a3}.{a2,a4}.{a3,a4}.{a1,a2,a3}.{a1,a2,a4}.{a1,a3,a4}.{a2,a3,a4}.{a1,a2,a3,a4}共16个子集
集合{a1,a2,a3 ....an}的子集的个数2的n次方
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