What are the concepts of union, intersection, difference and complement?

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1 Combine

remember A,B It's two sets , To belong to A Or of B The element of is a collection of elements called A And B And （ Set ）, Write it down as A∪B（ or B∪A）, pronounce as “A and B”（ or “B and A”）, namely A∪B={x|x∈A, or x∈B} .

2 intersection

remember A,B It's two sets , To belong to A And belongs to B The element of is a collection of elements called A And B Of （ Set ）, Write it down as A∩B（ or B∩A）, pronounce as “A hand over B”（ or “B hand over A”）, namely A∩B={x|x∈A, And x∈B}

3 Difference set

remember A,B It's two sets , Then all belong to A And it doesn't belong to B A collection of elements , It's called a collection A Subtractive set B( Or set A And assemble B The difference between the ), Similarly , For collection A、B, Assemble {x∣x∈A, And x∉B} be called A And B The difference between the set .

4 Complement set

remember A,U It's two sets , It belongs to the complete works U It doesn't belong to a collection A The set composed of elements of is called set A The complement of , Write it down as CuA, namely CuA={x|x∈U, And x Do not belong to A}.

5 Extended data

Morgan's law , Also called inversion law , It can be simply described as ： The complement of the intersection of two sets is equal to the union of their respective complements , The complement of the union of two sets is equal to the intersection of their respective complements .

If we gather A、B It's the whole book U Two subsets of , Then the following relationship is established ：

（1）∁U（A∩B）=（∁UA）∪（∁UB）, namely “ Make up for it ” be equal to “ Complement and merge ”;

（2）∁U（A∪B）=（∁UA）∩（∁UB）, namely “ Make up for it ” be equal to “ At the turn of mending ”

This paper is about joshua317 Original article , Reprint please indicate ： Reprinted from joshua317 Blog   Combine 、 intersection 、 Difference set 、 What is the concept of complement ？ - joshua317 The blog of