"Sufficient Conditions and Necessary Conditions" collection and common logical terms PPT (Lesson 1 Sufficient Conditions and Necessary Conditions)

"Sufficient Conditions and Necessary Conditions" collection and common logical terms PPT (Lesson 1 Sufficient Conditions and Necessary Conditions)

Part One: Learning Objectives

1. Understand the definitions of sufficient conditions and necessary conditions. (difficulty)

2. Can determine sufficient conditions and necessary conditions. (emphasis)

3. The value range of letters can be found based on sufficient and unnecessary conditions and necessary and insufficient conditions. (main difficulty)

core competencies

1. Improve logical reasoning skills through the judgment of sufficient conditions and necessary conditions.

2. Cultivate mathematical operation literacy through the application of sufficient conditions and necessary conditions.

Sufficient conditions and necessary conditions PPT, part 2: independent preview and exploration of new knowledge

A preliminary exploration of new knowledge

1. Sufficient and necessary conditions

Thinking 1: (1) Is the inference relationship represented by the sufficient condition that p is q and the necessary condition that q is p the same?

(2) The following five expression forms: ① p ⇒ q; ② p is a sufficient condition for q; ③ the sufficient condition for q is p; ④ q is a necessary condition for p; ⑤ the necessary condition for p is q. Are these five expression forms equivalent?

Tips: (1) are the same, both are p⇒q. (2) are equivalent.

2. Judgment of Sufficient and Necessary Conditions

3. The relationship between sufficient conditions, necessary conditions and sets

A＝{x|x satisfies condition p}, B＝{x|x satisfies condition q}

A⊆B p is a sufficient condition for q q is a necessary condition for p p is an insufficient condition for q q is an unnecessary condition for p

B⊆A q is a sufficient condition for p p is a necessary condition for q q is an insufficient condition for p p is an unnecessary condition for q

First try

1. Among the following propositions, q is a necessary condition for p ()

A． p：A∩B＝A，q：A⊆B

B. p: x2-2x-3=0, q: x=-1

C． p：|x|<1，q：x<0

D. p: x2>2, q: x>2

2. "x＝1" is () of "x2-1＝0"

A． Sufficient and unnecessary conditions

B. Necessary and insufficient conditions

C． Necessary and sufficient conditions

D. Neither sufficient nor necessary conditions

3. "△ABC is a right triangle" is the ________ condition of "its three-side relationship a2+b2=c2". (Fill in “sufficient” or “necessary”)

4. "x2=2x" is the ________ condition of "x=0", and "x=0" is the ________ condition of "x2=2x". (Fill in the blanks with "sufficient" and "necessary")

Sufficient conditions and necessary conditions PPT, the third part: cooperative exploration to improve literacy

Judgment of sufficient conditions and necessary conditions

[Example 1] In the following proposition of the form "if p, then q", what condition is there for p to be q? (Sufficient and unnecessary conditions, necessary and insufficient conditions, both sufficient and necessary conditions, neither sufficient nor necessary conditions)

(1) If x=1, then x2-4x+3=0;

(2) If the function y=x, the function is increasing;

(3) If x is an irrational number, then x2 is an irrational number;

(4) If x=y, then x2=y2;

(5) If two triangles are congruent, then the areas of the two triangles are equal;

(6) If a>b, then ac>bc.

regular method

The six questions in this example respectively reflect the definition method, the set method, and the equivalence method. Generally speaking, the definition method is mainly used for simpler proposition judgments, the set method generally needs to simplify propositions, and the equivalence method is mainly used for negation. Sexual proposition. To judge whether p is a sufficient condition for q, we must see whether p can deduce q. To judge whether p is a necessary condition for q, we must see whether q can deduce p.

The relationship between sufficient conditions, necessary conditions and sets

[Example 2] If "x2>1" is a necessary and insufficient condition for "x

[Solution]∵x2>1, ∴x<-1 or x>1.

And ∵ “x2>1” is a necessary and insufficient condition for “x

∴x1 but x2>1D⇒/x

∴a≤-1, the maximum value of ∴a is -1.

regular method

Suppose the set A={x|x satisfies p}, B={x|x satisfies q}, then p⇒q can get A⊆B; q⇒p can get B⊆A; p⇔q can get A=B, if p is a sufficient and unnecessary condition of q, then A is a proper subset of B.

Application of sufficient and necessary conditions

[Example 3] (1) "x2=4" is a necessary condition for "x=m", then a value of m can be ()

A． 0B. 2C. 4D. 16

(2) It is known that p: -4

regular method

Two ideas of applying sufficient conditions and necessary conditions

1 Conditions and conclusions: Determine which of p and q is the condition and which is the conclusion.

2 Application of p⇒q and q⇒p: Sufficient conditions ensure that p⇒q is true, and necessary conditions ensure that q⇒p is true.

Class summary

1. How to judge sufficient conditions and necessary conditions

(1) Definition method: directly use the definition to make judgments.

(2) Equivalence method: "p⇔q" means that p is equivalent to q. The equivalent proposition can be converted. When we want to prove that p is true, we can prove that q is true.

(3) Use the inclusion relationship between sets to make judgments: If the corresponding sets of condition p and conclusion q are A and B respectively, then if A⊆B, then p is a sufficient condition for q; if A⊇B, then p is q Necessary condition of q; if A=B, then p is both a sufficient condition and a necessary condition of q.

2. When finding the value range of parameters based on sufficient conditions and necessary conditions, the problem is transformed into the inclusion relationship between the corresponding two sets based on the relationship between sufficient conditions, necessary conditions and sets, and then the inequalities (groups) about the parameters are established. ) to solve.

Sufficient conditions and necessary conditions PPT, the fourth part: reaching the standard in court and solidifying the double base

1. "Equal angles" means "two straight lines are parallel" ( )

A． Sufficient and unnecessary conditions

B. Necessary and insufficient conditions

C． It is both a sufficient condition and a necessary condition

D. Neither sufficient nor necessary conditions

2. A sufficient condition for x>3 to hold is ( )

A． x>4　B． x>0

C． x>2 D. x<2

3. Assume x, y∈R, then "x≥2 and y≥2" is () of "x2＋y2≥4"

A． Sufficient and unnecessary conditions B. Necessary and insufficient conditions

C． Necessary and sufficient conditions D. Neither sufficient nor necessary conditions

4. There are the following inequalities: ①x<1; ②0

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