"Sufficient Conditions and Necessary Conditions" collection and common logical terms PPT download

Description

"Sufficient Conditions and Necessary Conditions" collection and common logical terms PPT download

Part One: Learning Objectives

1. Combined with specific examples, understand the meaning of sufficient conditions, necessary conditions, and necessary and sufficient conditions. (main difficulty)

2. Be able to find (judge) the sufficient conditions, necessary conditions, and necessary and sufficient conditions for the establishment of certain problems. (emphasis)

3. Be able to use the relationship between propositions to determine the necessary and sufficient relationship or to prove the necessary and sufficient conditions. (difficulty)

core competencies

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

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

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

A preliminary exploration of new knowledge

1. Sufficient and necessary conditions

The proposition is true or false. "If p, then q" is a true proposition. "If p, then q" is a false proposition.

Push out the relation pq P___q

Conditional relationship p is the condition of q q is the condition of p

p is not the condition of q q is not the condition of p

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?

2. Necessary and Sufficient Condition

(1) Generally, if there is both p⇒q and q⇒p, it is recorded as p⇔q. At this time, we say that p is the ________ condition of q, referred to as the ________ condition.

In summary, if p⇔q, then p and q________ conditions.

(2) If p⇒q, but q p, then p is said to be a sufficient and unnecessary condition of q.

(3) If q⇒p, but p q, then p is said to be a necessary and insufficient condition of q.

(4) If p q, and q p, then it is neither sufficient nor necessary to say that p is a condition of q.

Thinking 2: (1) If p is a necessary and sufficient condition for q, then propositions p and q are two mutually equivalent propositions. Is this correct?

(2) What is the difference between "p is a necessary and sufficient condition for q" and "a necessary and sufficient condition for p is q"?

First try

1. Which of the following statements is a proposition ( )

A． A trapezoid is a quadrilateral

B． Draw straight line AB

C. x is an integer

D. will it snow today

2. "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

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

A． x>4

B． x>0

C. x>2

D. x<2

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

Judgment of sufficient conditions and necessary conditions

【Example 1】Indicate the conditions under which p is q in each of the following questions.

(1)p: x-3=0, q: (x-2)(x-3)=0.

(2)p: Two triangles are similar, q: Two triangles are congruent.

(3)p: a>b, q: ac>bc.

[Solution] (1)x-3＝0⇒(x-2)(x-3)＝0, but (x-2)(x-3)＝0 x-3＝0, Therefore, p is a sufficient and unnecessary condition of q.

(2) Two triangles are similar. Two triangles are congruent, but two triangles are congruent ⇒ two triangles are similar, so p is a necessary and insufficient condition for q.

(3) a>b ac>bc, and ac>bc a>b,

Therefore, p is neither a sufficient nor necessary condition for q.

regular method

Definition method to determine sufficient and necessary conditions

1Determine who is the condition and who is the conclusion

2Try to deduce the conclusion from the conditions. If the conditions can deduce the conclusion, then the conditions are sufficient conditions. Otherwise, they are not sufficient conditions.

3Try to deduce the condition from the conclusion. If the conclusion can deduce the condition, then the condition is a necessary condition, otherwise it is not a necessary condition.

Track training

1. Indicate the conditions under which p is q in each of the following sets of propositions.

(1)p: The diagonals of a quadrilateral are equal, q: The quadrilateral is a parallelogram.

(2)p: (x-1)2+(y-2)2=0, q: (x-1)(y-2)=0.

[ Solution

(2) Because (x-1)2+(y-2)2=0⇒x=1 and y=2⇒(x-1)(y-2)=0, and (x-1)(y-2 )=0 (x-1)2+(y-2)2=0, so p is a sufficient and unnecessary condition of q.

Application of sufficient conditions, necessary conditions and necessary and sufficient conditions

[Inquiry Questions]

1. Remember the set A={x|p(x)}, B={x|q(x)}. If p is a sufficient and unnecessary condition of q, what is the relationship between sets A and B? What if p is a necessary or insufficient condition for q?

Tip: If p is a sufficient and unnecessary condition of q, then A B. If p is a necessary and insufficient condition of q, then B A.

2. Note that the set M={x|p(x)}, N={x|q(x)}, if M⊆N, what condition does p have for q? What if N⊆M, M=N?

Tip: If M⊆N, then p is a sufficient condition for q. If N⊆M, then p is a necessary condition for q. If M=N, then p is a necessary and sufficient condition for q.

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

1. Thinking and analysis

(1) When q is a necessary condition for p, p is a sufficient condition for q. ()

(2) When q is not a necessary condition for p, “p q” holds. ()

(3) If q is a necessary condition for p, then q holds and p also holds. ()

2. "x>0" is ( ) of "x≠0"

A． Sufficient and unnecessary conditions

B． Necessary and insufficient conditions

C. Necessary and sufficient conditions

D. Neither sufficient nor necessary conditions

3. The necessary and sufficient condition for the graph of function f(x)=x2+mx+1 to be symmetrical about the straight line x=1 is ________.

Keywords: Free download of PPT courseware for the compulsory course I of Mathematics in High School People's Education A version, PPT download of sufficient conditions and necessary conditions, PPT download of sets and common logical terms, .PPT format;

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Update Time: 2024-07-28

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

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