"The Concept of Sets" Sets and Common Logic Terms PPT (Representation of Sets in Lesson 2)

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"The Concept of Sets" Sets and Common Logic Terms PPT (Representation of Sets in Lesson 2)

Part One: Learning Objectives

1. Preliminarily master the two representation methods of sets - enumeration method and description method, and feel the meaning and function of set language. (emphasis)

2. Be able to express some simple sets using two representation methods of sets. (main difficulty)

core competencies

1. Cultivate the quality of mathematical abstraction by learning the method of describing sets.

2. Cultivate the literacy of mathematical operations by using the operations when converting description method into enumeration method.

The concept of collection PPT, the second part of the content: independent preview and exploration of new knowledge

A preliminary exploration of new knowledge

1. Enumeration method

The method of _________ out all the elements of a set and enclosing them in _________ is called the enumeration method.

2. descriptive method

Generally speaking, assuming A is a set, the set composed of all elements x with ________P(x) in set A is represented as {x∈A|P(x)}. This method of representing a set is called Description method.

Thinking: (1) What common characteristics do the elements in the solution set of the inequality x-2<3 have in common?

(2) How to use description method to express the solution set of inequality x-2<3?

Tips: (1) The common characteristics of the elements are x∈R, and x<5.

(2){x|x<5, x∈R}.

First try

1. The solution set of equation x2=4 is expressed as () by enumeration method

A． {(-2,2)} B． {-2,2}

C. {-2} D. {2}

2. The description method that expresses all points on the graph of function y=3x+1 is ()

A． {x|y＝3x＋1}

B． {y|y＝3x+1}

C. {(x,y)|y＝3x+1}

D. {y＝3x＋1}

3. Use descriptive method to express the solution set of inequality 4x-5<7 as ________.

The concept of collection PPT, the third part of the content: cooperative exploration to improve literacy

Represent sets using enumeration

[Example 1] Use enumeration method to express the following given set:

(1) A set A consisting of non-negative even numbers not greater than 10;

(2) The set B composed of prime numbers less than 8;

(3) The set C composed of real roots of the equation 2x2-x-3=0;

(4) The set D composed of the intersection points of the graphs of linear functions y=x+3 and y=-2x+6.

[Solution] (1) The non-negative even numbers not greater than 10 are 0,2,4,6,8,10, so A={0,2,4,6,8,10}.

(2) Prime numbers less than 8 include 2, 3, 5, and 7.

So B={2,3,5,7}.

(3) The real roots of equation 2x2-x-3=0 are -1,32,

So C=-1,32.

regular method

3 steps to represent sets using enumeration

1Find the elements of the set;

2List the elements one by one, and the same element can only be listed once;

3Enclose it in curly braces.

Reminder: The solution set of a system of binary equations and the set of points on the function graph are all sets of points. They must be written in the form of real number pairs, and the elements are separated by ",". For example, {2, 3 ,5,-1}.

The concept of collection PPT, the fourth part of the content: reaching the standard and solidifying the two bases in the hall

1. Thinking and analysis

(1){1}＝1.()

(2){(1,2)}={x=1, y=2}. ()

(3){x∈R|x>1}={y∈R|y>1}. ()

(4){x|x2＝1}＝{-1,1}. ()

2. The set consisting of even numbers greater than -3 and less than 11 is ()

A． {x|－3

B． {x|－3

C. {x|-3

D. {x|-3

3. The set of intersection points of the graphs of linear functions y=x-3 and y=-2x is ()

A． {1,-2}

B． {x=1, y=-2}

C. {(-2,1)}

D. {(1,-2)}

4. Suppose the set A={x|x2-3x+a=0}, if 4∈A, use the enumeration method to express the set A.

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Update Time: 2024-06-05

This template belongs to Mathematics courseware People's Education High School Mathematics Edition A Compulsory Course 1 industry PPT template

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