集合定义

Set（集合）-collection of distinct objects

Element（元素）-each object in the set

Empty Set（空集）-a set does not contain any elements, symbol: ø

Subset（子集）-for two sets A and B, if B contains all the elements of A, then A is a subset of B

Universal Set（全集）-the set contains all the elements of the situation under consideration

Complement（补集）-in a universal set, the complement of the set A A' is the set of all the elements that do not belong to A

Venn Diagram（韦恩图）-diagrams drawn below️, used to show the relationships between sets

Venn diagrams

Union（并集）-the union of two sets is the set of all the elements that belong to either one of the set or the other or both

Intersection（交集）-the intersection of two sets is the set of all the elements that belong to both

Union&Intersection

当集合被用于概率性研究

Possible Outcomes -所有可能结果，如图A与B'的交集，其Possible outcomes即黑点、白点和星星；图A'并B'中，possible outcome就只有白点

Sample Space (S) -formed by all of the possible outcomes

Favorable Outcome -特定结果，如A交B'中，favorable outcome就是黑点，而A'与B'的并集中，没有favorable outcome

Event (E) -a subset of the sample space, representing a specific outcome or a combination of outcomes.

Impossible Event -contains no outcomes, 在韦恩图中是个空集

Using Set Language in Possibility

Mutually Exclusive Events -two sets that cannot occur at the same time, 韦恩图中两个集合不会相交重合

Non-mutually Exclusive Events -two sets that can occur at the same time, 韦恩图中两个集合会相交重合

Mutually Exclusive Events&Non-mutually Exclusive Events

Complementary Event -如下图，从universal set U中抽取elements, 抽到的不是黑点就会是白点，不会有第三种情况。这种情况就是两个事件互为complementary events。在Venn Diagram中，这两个setsA'与B'的交集并A与B的交集和A与B'的交集并A'与B的交集互为complementary sets。