First, the concept of principles and rule sets

1. set: a whole composed of some objects, which is called a set for short. The objects that make up a set are called elements of this set. 2. the relationship between element a and set a: ①a? A (element A belongs to set A) 2a? A (element A does not belong to set A) 3. Ordinary number set: natural number set n positive integer set *

Integer set z rational number set q real number set r

4. A set without any elements is called an empty set, and it is recorded as? 5. Representation of sets: enumeration and description.

① Enumeration: enumerate the elements of the collection one by one, separate them with commas, and then enclose them with curly braces as a whole. The solution set of the equation is expressed by enumeration. Description: draw a vertical line with braces, write the representative element X of the set on the left side of the vertical line, mark the value range of the element, and write the characteristic properties of the element on the right side of the vertical line. Represent the solution set of inequality by descriptive method. Second, ★ the relationship between sets ★

1. Equal: the elements in set A and set B are exactly the same. Write A=B

2. Subset: If any element in A belongs to B, A is called a subset of B ... Write: A? B(A is contained in B) or B? A(B) contains a) 3. Proper subset: A is a subset of B, and at least one element in B does not belong to A Note: A B(A really contains B) or B A(B really contains A).

* * * * * Calculation of the number of elements in the set: If there are n elements in the set A, the number of all different subsets of the set A is * * * * * * * All proper subset numbers are _ _ _ _ _ _ _ _, and all non-empty proper subset numbers are three. ★ Operation of the unit ★

1. intersection: a ∩ b = {x2008x ∈ a and x∈B} Take the same elements of set A and set B.

2. Union: A∪B={x 丨∈ a or x∈B} Combines all elements in set A and set B, and only records the repeated elements 1 time.

3. Complement set: acu = {x x ∈ u and x? A} The set whose elements in set A are removed from the complete set U is the complement set ACU IV, if and only if ★

1. Necessary and sufficient condition: Condition P holds? Conclusion Q is true and P is true? Conclusion q holds. 2. Necessary and sufficient conditions: Is condition P true? Conclusion Q is true and P is true? Conclusion q holds. 3. Necessary and sufficient conditions: Is condition P true? Conclusion q holds.