1, definition of set, representation of common set (n, z, q, r), empty set. The three elements of a set, the expression method and the relationship between the elements and the set;

2. The relationship between sets (including, really containing, equal to, that is, subset, proper subset, equal to).

3. Operations between sets (intersection, union and complement)

4. The operation formula between commonly used sets:

1. idempotent law: A∪A=A, a ∪ a = a.

2. identity: a ∪ φ = a ∪φ = a ∪ u = a.

3. complementary law: A∪A'=U, A∪A' =φ (where a' stands for the complement of a).

4 commutative law: A∪B=B∪A, a ∪ b = b ∪ a.

5. Law of association: (A∪B)∪C=A∪(B∪C), (A∪B)∩C = A ∪( B∪C).

6. Distribution law: A∩(B∩C)=(A∪B)∩(A∪C), A ∪( B∪C)=(A∪B)∪( A).

7. law of absorption: A∩(A∩B)= A, a ∩ (a ∪ b) = a.

8. Inverse law: (A∪B)' = A '∪B', (A∪B)' = A '∪B'

Second, the function:

1, function definition (this must remember the key words and understand)

2. Representation of functions (pay attention to piecewise functions)

3. The domain, range and three elements of a function, and the conditions for the equality of functions.

4. The properties of the function: (1) monotonicity (pay attention to the definition and local properties) and maximum value (after monotonicity, you want to use monotonicity to find the maximum value); (2) parity (understanding the definition, the overall nature); (3) From parity to functional symmetry (central symmetry and axial symmetry).