幂集和并集
给出以下集合：
X := {Horse, Dog}
Y := {Cat}
我定义集合：
M := Pow(X) u {Y}
u 表示并集 幂
集运算的结果集是：
Px := {0, {Horse}, {Dog}, {Horse, Dog}}
0 表示空集
我的问题引用了 unio 操作。 如何将 0 和 Y 结合起来？
M := {{Horse, Cat}, {Dog, Cat}, {Horse, Dog, Cat}}
Following set is given:
X := {Horse, Dog}
Y := {Cat}
I define the set:
M := Pow(X) u {Y}
u for union
The resulting set of the power set operation is:
Px := {0, {Horse}, {Dog}, {Horse, Dog}}
0 for empty set
My question is referenced to the unio operation. How do I unite 0 and Y?
M := {{Horse, Cat}, {Dog, Cat}, {Horse, Dog, Cat}}
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我将与其他答案略有不同。如果定义
Y = {Cat}则{Y} = {{Cat}}，即Y是包含该元素的集合Cat和{Y}是包含Y的集合，或者包含包含元素Cat的集合的集合。在这种情况下：这是集合论中一个微妙但重要的区别。
I'm going to differ slightly with the other responses. If you define
Y = {Cat}then{Y} = {{Cat}}, that is,Yis the set containing the elementCatand{Y}is the set containingY, or the set containing the set containing the elementCat. In that case:It's a subtle, but important distinction in set theory.
你有
这样
的
事情吗？这对你来说清楚了吗？
您显示的集合映射到笛卡尔积并缺少
{Cat}。you have
with
so
Does that clear it up for you?
The set you've displayed the union mapped over the cartesian product and missing
{Cat}.并集的定义是任一集合中的元素集合。因此
{Horse,Cat}不在联合中，因为它不在任一集合中。The definition of the union is the set of elements that are in either set. So
{Horse,Cat}is not in the union, because it is not in either set.