Set up the vOut Strategy

Slides:

Advertisements

Similar presentations

AB 11 22 33 44 55 66 77 88 99 10  20  19  18  17  16  15  14  13  12  11  21  22  23  24  25  26  27  28.

Advertisements

EXAMPLE 4 Prove the Converse of the Hinge Theorem

Corresponding Parts of Congruent Triangles Congruent Using Congruent Triangles : CPCTC Corresponding Parts of Congruent Triangles Congruent Geometry 5.0.

>In We need a rule that will let us prove a conditional. What should the rule be?

Proving Segment Relationships

Proving Segment Relationships Postulate The Ruler Postulate The points on any line or line segment can be paired with real numbers so that, given.

Fig. 16-CO, p Fig. 16-1, p. 450 Fig. 16-2, p. 450.

IEEE Spice Seminar Simulation Program with Integrated Circuit Emphasis.

Animales domésticos BV Educación

Isosceles Triangles. If 2 sides are congruent The angles opposite those sides are congruent.

Miss Battaglia BC Calculus. Alternative limit form of the derivative: provided this limit exists. Note the limit in this alternative form requires that.

Section 1-3 Segments, Rays, and Distance. line; segment; ray;

Section 1.3 Segments & Their Measures 1/14. Geometric Vocabulary Postulate : Rules that are accepted without proof. Axiom : Synonym for postulate. Theorem.

Triangle Congruence: by SSS and SAS Geometry H2 (Holt 4-5) K. Santos.

Geometry Unit 2: Reasoning and Proof.  Proof with numbered statements and reasons in logical order.

1S Algebra Revision! $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400.

Slide 1Fig 28-CO, p.858. Slide 2Fig 28-1, p.859 Slide 3Fig Q28-19, p.884.

Wedge In1 (vIn) 1 1. (FvA) > G A[1] 1 F > GGOAL[2]

 Geometric mean of any n numbers is:  Find the geometric mean of the following list of numbers. A. 4, 6 B. 3, 5, 9 C. 4, 8, 10, 12.

Wedge Out (vOut) BIG MISTAKE: 1. PvQ 2. P 1 vO Wedge Out (vOut) BIG MISTAKE: 1. PvQ 2. P 1 vO This is NOT vOut, and besides... the reasoning is INVALID!

We can also use the Distributive Property in reverse. This is called Factoring. When we factor an expression, we find all numbers or variables that divide.

 ESSENTIAL QUESTION  How can you prove a mathematical statement?  Scholars will..  Write proofs involving segment addition.  Write proofs involving.

Objective: To prove and apply theorems about angles Proving Angles Congruent (2-6)

Geometric Proof GCSE Higher. Prove that the sum of the angles in a triangle is 180° A C B We can use previous knowledge of the properties of parallel.

2.5 Reasoning and Algebra. Addition Property If A = B then A + C = B + C.

Study Questions for Quiz 7 The exam has three parts: 1. (45 pts) Argument Translation in Predicate Logic 2. (65 pts) Proofs and Trees in Predicate Logic.

Station 1 – Provide a justification (definition, property, postulate, or theorem) for each statement. D 1.) If BH ^ DC, then ÐDCH is a right angle. 2.)

Have your homework out and be in your seat when the bell rings!

Lesson 2 – 7 Proving Segment Relationships

5.6 Comparing Measures of a Triangle

Reasoning in Algebra and Geometry

4.8 Triangles and Coordinate Proofs

Write a two-column proof

2.5 and 2.6 Properties of Equality and Congruence

The open loop gain of this op-amp is 105 and the bandwidth is 10 Hz

Unit 1 Day 10 TWO COLUMN PROOFS.

Set up ratios: = = Fill in ratios: Solve the proportion: =

Top 6 Strategies of Digital Marketing.

2. Definition of congruent segments AB = CD 2.

Ways to Prove Triangles Congruent

Direct Proof and Counterexample III

Recall Lecture 6 Rectification – transforming AC signal into a signal with one polarity Half wave rectifier Full Wave Rectifier Center tapped Bridge Rectifier.

The points A and B are opposite corners of a rectangle.

מסננים מסנן מעביר נמוכים LPF תומר ורונה.

The Distributive Property

&In and &Out The rules for & are very simple. A A&B A&B

Chapter 1 Exploring Geometry: Points, Lines, and Angles in the Plane

Operational Amplifier (Op-Amp)-μA741

More Complex Proofs 1. TvP A 2. -P A T GOAL.

AC Transformers Source: OSHA.

Strategy Review Here is a summary of all the

Strategy Review Here is a summary of all the

Put CW/HW on the corner of your desk!

Review of Triangle Congruence Figures and PROOFS

Parallel lines and transversals

TPS54620 Current Limit J. Tucker 5 June, 2018.

#17 PA8 Sem2 Practice Exam A #17 PA8 Sem2 Practice Exam B

Properties of Triangles

Dependency Lists Whenever you use PA in a proof,

A very difficult problem There is nothing to do, so try -Out.

K.CC.6 Comparing Numbers If one student provides an answer it is important for the teacher to continue the discussion on this problem by prompting students.

10k 20k Vin Vout H3 What is the gain?

Lines, rays and line segments

Review Questions 3rd OA.5.

strategic advice given for Chapters

Do Now: Below is a proof given by a student. Evaluate the student’s proof by giving it a score out of 10 points, explaining your score (ie, what was good.

Sample Proofs 1. S>-M A 2. -S>-M A -M GOAL.

Presentation transcript:

Set up the vOut Strategy Proofs Using vOut 1. V v -V A 2. V>-B A 3. -V>-N A -Bv-N GOAL A v B A>G B>G G A v B G Set up the vOut Strategy

... by making the missing conditionals new goals. Proofs Using vOut 1. V v -V A 2. V>-B A 3. -V>-N A -Bv-N GOAL A v B A>G B>G G A v B G ... by making the missing conditionals new goals.

Prove the top goal using the >I Strategy Proofs Using vOut 1. V v -V A 2. V>-B A 3. -V>-N A V>(-Bv-N) GOAL -V>(-Bv-N) GOAL -Bv-N 1,?,? vO A v B A>G B>G G A v B G Prove the top goal using the >I Strategy

Apply >O whenever you can. Proofs Using vOut 1. V v -V A 2. V>-B A 3. -V>-N A 4. V PA -Bv-N GOAL V>(-Bv-N) 4-? >I -V>(-Bv-N) GOAL -Bv-N 1,?,? vO A v B A>G B>G G A v B G Apply >O whenever you can.

... and your goal comes by vIn Proofs Using vOut 1. V v -V A 2. V>-B A 3. -V>-N A 4. V PA -B 2,4 >O -Bv-N GOAL V>(-Bv-N) 4-? >I -V>(-Bv-N) GOAL -Bv-N 1,?,? vO A v B A>G B>G G A v B G ... and your goal comes by vIn

Now use >In to obtain your second goal. Proofs Using vOut 1. V v -V A 2. V>-B A 3. -V>-N A 4. V PA 5. -B 2,4 >O 6. -Bv-N 5 vI 7. V>(-Bv-N) 4-6 >I -V>(-Bv-N) GOAL -Bv-N 1,7,? vO A v B A>G B>G G A v B G Now use >In to obtain your second goal.

Apply >O whenever you can. Proofs Using vOut 1. V v -V A 2. V>-B A 3. -V>-N A 4. V PA 5. -B 2,4 >O 6. -Bv-N 5 vI 7. V>(-Bv-N) 4-6 >I 8. -V PA -Bv-N GOAL -V>(-Bv-N) 8-? >I -Bv-N 1,7,? vO A v B A>G B>G G A v B G Apply >O whenever you can.

... and your goal comes by vIn Proofs Using vOut 1. V v -V A 2. V>-B A 3. -V>-N A 4. V PA 5. -B 2,4 >O 6. -Bv-N 5 vI 7. V>(-Bv-N) 4-6 >I 8. -V PA -N 3,8 >O -Bv-N GOAL -V>(-Bv-N) 8-? >I -Bv-N 1,7,? vO A v B A>G B>G G A v B G ... and your goal comes by vIn

The proof is now complete. Proofs Using vOut 1. V v -V A 2. V>-B A 3. -V>-N A 4. V PA 5. -B 2,4 >O 6. -Bv-N 5 vI 7. V>(-Bv-N) 4-6 >I 8. -V PA 9. -N 3,8 >O 10. -Bv-N 9 vI 11. -V>(-Bv-N) 8-10>I 12. -Bv-N 1,7,11 vO A v B A>G B>G G A v B G The proof is now complete.

Do &Out whenever you can Proofs Using vOut A v B G A v B A>G B>G G 1. A&(BvC) A (A&B)v(A&C) GOAL Do &Out whenever you can

Set up the vOut Strategy Proofs Using vOut A v B G A v B A>G B>G G 1. A&(BvC) A 2. A 1 &O 3. B v C 1 &O (A&B)v(A&C) GOAL Set up the vOut Strategy

Set the missing conditionals as new goals. Proofs Using vOut A v B G A v B A>G B>G G 1. A&(BvC) A 2. A 1 &O 3. B v C 1 &O (A&B)v(A&C) 3,?,? vO Set the missing conditionals as new goals.

Use >In to prove the first goal. Proofs Using vOut A v B G A v B A>G B>G G 1. A&(BvC) A 2. A 1 &O 3. B v C 1 &O B >[(A&B)v(A&C)] GOAL C >[(A&B)v(A&C)] GOAL (A&B)v(A&C) 3,?,? vO Use >In to prove the first goal.

Prove A&B so that you can use vIn to obtain the goal. Proofs Using vOut A v B G A v B A>G B>G G 1. A&(BvC) A 2. A 1 &O 3. B v C 1 &O 4. B PA (A&B)v(A&C) GOAL B >[(A&B)v(A&C)] 4-? >I C >[(A&B)v(A&C)] GOAL (A&B)v(A&C) 3,7,? vO Prove A&B so that you can use vIn to obtain the goal.

Now the subproof can be completed with vIn. Proofs Using vOut A v B G A v B A>G B>G G 1. A&(BvC) A 2. A 1 &O 3. B v C 1 &O 4. B PA 5. A&B 2,4 &I (A&B)v(A&C) GOAL B >[(A&B)v(A&C)] 4-? >I C >[(A&B)v(A&C)] GOAL (A&B)v(A&C) Now the subproof can be completed with vIn.

Now set up the >In Strategy to prove the second goal. Proofs Using vOut A v B G A v B A>G B>G G 1. A&(BvC) A 2. A 1 &O 3. B v C 1 &O 4. B PA 5. A&B 2,4 &I 6. (A&B)v(A&C) 5 vI 7. B >[(A&B)v(A&C)] 4-6 >I C >[(A&B)v(A&C)] GOAL (A&B)v(A&C) 3,7,? vO Now set up the >In Strategy to prove the second goal.

This subproof can be completed in the same way. Proofs Using vOut A v B G A v B A>G B>G G 1. A&(BvC) A 2. A 1 &O 3. B v C 1 &O 4. B PA 5. A&B 2,4 &I 6. (A&B)v(A&C) 5 vI 7. B >[(A&B)v(A&C)] 4-6 >I 8. C PA (A&B)v(A&C) GOAL C >[(A&B)v(A&C)] 8-? >I (A&B)v(A&C) 3,7,? vO This subproof can be completed in the same way.

The proof is now complete. Proofs Using vOut A v B G A v B A>G B>G G 1. A&(BvC) A 2. A 1 &O 3. B v C 1 &O 4. B PA 5. A&B 2,4 &I 6. (A&B)v(A&C) 5 vI 7. B >[(A&B)v(A&C)] 4-6 >I 8. C PA 9. A&C 2,8 &I 10. (A&B)v(A&C) 9 vI 11. C >[(A&B)v(A&C)] 8-10 >I 12. (A&B)v(A&C) 3,7,11 vO The proof is now complete.