"End-of-Chapter Review and Improvement Course" Collection and Commonly Used Logic Phrases PPT

"End-of-Chapter Review and Improvement Course" Collection and Commonly Used Logic Phrases PPT

Part One Content: Comprehensive Improvement

Basic concepts of collections

(1) It is known that the set A = {0, 1, 2}, then the number of elements in the set B = {x-y|x∈A, y∈A} is ()

A． 1B. 3

C． 5 D． 9

(2) If -3∈{x-2, 2x2-5x, 12}, then x=________.

[Analysis] (1) ① When x=0, y=0, 1, 2, the values ​​of x-y at this time are 0, -1, -2 respectively;

②When x=1, y=0, 1, 2, the values ​​of x-y are 1, 0, -1 respectively;

③When x=2, y=0, 1, 2, the values ​​of x-y are 2, 1, 0 respectively.

In summary, it can be seen that the possible values ​​of x-y are -2, -1, 0, 1, 2, a total of 5, so choose C.

(2) From the meaning of the question, x-2=-3 or 2x2-5x=-3.

①When x-2=-3, x=-1.

Substituting x = -1, the three elements of the set are -3, 7, and 12, which satisfy the mutuality of the elements in the set;

regular method

Two points that should be paid attention to when solving conceptual problems of sets

(1) To study a set, we must first look at the representative elements in the set, and then look at the limiting conditions of the elements. When the set is represented by a descriptive method, pay attention to clarifying the meaning of its elements. For example, in this example (1), the elements in set B are real numbers, and some are pairs of numbers (point sets).

(2) For a set containing letters, after calculating the value of the letters, attention should be paid to checking whether the elements satisfy mutuality.

Basic relations of sets

It is known that the set A={x|x<-1 or x≥1}, B={x|2a

regular method

(1) Two common methods for judging the relationship between two sets

The first is to simplify the sets and find the relationship between the two sets from the expression; the second is to use the enumeration method to express each set and find the relationship from the elements.

(2) Key points in dealing with relationship issues between sets

When the relationship between two sets is known and parameters are obtained, the key is to transform the relationship between the two sets into a relationship between elements, and then into a relationship that satisfies the parameters. Solving such problems often requires the rational use of number lines and Venn diagrams to help analyze. At the same time, we should also pay attention to the "trap" of "empty set". Especially when the set contains alphabetic parameters, we must classify and discuss them, and do not omit any important items during the discussion.

Set operations

(1) Suppose the set A={1, 2, 4}, B={x|x2-4x+m=0}. If A∩B={1}, then B=()

A． {1,-3}B. {1,0}

C． {1,3} D. {1,5}

(2) Let the complete set be R, set A={x|3≤x<6}, B={x|2

① Find A∩B, (∁RB)∪A respectively;

② It is known that C={x|a

regular method

(1) Methods of basic operations on sets

① Definition method or Venn diagram method: The set is given by the enumeration method, and the operation can be solved directly with the help of definitions, or the elements can be represented in a Venn diagram and solved with the help of Venn diagram observation;

② Number axis method: The set is given by an inequality (group). During operation, the inequality can be expressed on the number axis first, and then the solution can be solved with the help of the number axis.

(2) Types and solutions of operations combining sets and inequalities

① No letter parameters: directly solve the inequalities in the set and solve on the number axis;

②Contains letter parameters: If the value of letters affects the solution of the inequality, the letters must be classified and discussed first, then the inequality is solved, and then the solution is solved on the number axis.

End-of-Chapter Review Improvement Lesson PPT, Part 2 Content: Literacy Improvement

1. It is known that the set A={x|2x-3<3x}, B={x|x≥2}, then ()

A． A⊆BB. B⊆A

C． A⊆∁RB D. B⊇∁RA

2. It is known that the set A={x|x+1>0}, B={-2,-1,0,1}, then (∁RA)∩B=()

A． {-2,-1} B． {-2}

C． {-1, 0, 1} D． {0,1}

3． It is known that A and B are both subsets of the set U={1, 3, 5, 7, 9}, and A∩B={3}, (∁UB)∩A={9}, then A=()

A． {1,3} B. {3,7,9}

C． {3, 5, 9} D. {3,9}

4. It is known that a, b, c are real numbers. Which of the following propositions is correct? ()

A． "a2>b2" is a sufficient condition for "a>b"

B. "a2>b2" is a necessary condition for "a>b"

C． "ac2>bc2" is a sufficient condition for "a>b"

D. "|a|>|b|" is a necessary and sufficient condition for "a>b"

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