Upload File

if-then statements. a statement in two parts hypothesis and conclusion. written in the if-then form...

  • Home
  • Documents
  • If-Then Statements. A statement in two parts Hypothesis and Conclusion. Written in the If-Then form If..Hypothesis, then… Conclusion
24
2.1 Conditional Statements If-Then Statements

Upload: orlando-sullins

Post on 01-Apr-2015

222 views

Category:

Documents


1 download

Report

TRANSCRIPT

Page 1: If-Then Statements. A statement in two parts Hypothesis and Conclusion. Written in the If-Then form If..Hypothesis, then… Conclusion

2.1 Conditional Statements

If-Then Statements

Page 2: If-Then Statements. A statement in two parts Hypothesis and Conclusion. Written in the If-Then form If..Hypothesis, then… Conclusion

A statement in two parts Hypothesis and Conclusion.

Written in the If-Then form If ..Hypothesis, then… Conclusion

Conditional Statement

Page 3: If-Then Statements. A statement in two parts Hypothesis and Conclusion. Written in the If-Then form If..Hypothesis, then… Conclusion

“If you don’t eat your meat, then you can’t have any pudding”◦ Pink Floyd

If you study the notes in Geometry, then you have a much better chance of passing a test or quiz.- Me

If - then

Page 4: If-Then Statements. A statement in two parts Hypothesis and Conclusion. Written in the If-Then form If..Hypothesis, then… Conclusion

If x = 3, then x + 4 = 7

x = 3 is the hypothesis; label as p

x + 4 = 7 is the conclusion; label as q

If p then q

Here another conditional statement

Page 5: If-Then Statements. A statement in two parts Hypothesis and Conclusion. Written in the If-Then form If..Hypothesis, then… Conclusion

If the hypothesis is not true, then strange things will happen.

“If pigs fly, then I will win the Lottery”.

The Hypothesis must always be TRUE

Page 6: If-Then Statements. A statement in two parts Hypothesis and Conclusion. Written in the If-Then form If..Hypothesis, then… Conclusion

Counter Examples are very powerful. With one counter example you can stop an argument with one thought.

“If everyone likes snow days, then everyone likes cold weather”

Is there someone here in the class that does not like cold weather?

The Counter Example

Page 7: If-Then Statements. A statement in two parts Hypothesis and Conclusion. Written in the If-Then form If..Hypothesis, then… Conclusion

If x2 = 25, then x = 5Is this true? (5)2 = 25

but the counter example shows ( - 5)2 = 25

So the conditional statement is false. Since – 5 would also work.

Conditional statements can be true or false.

An Algebra Counter Example

Page 8: If-Then Statements. A statement in two parts Hypothesis and Conclusion. Written in the If-Then form If..Hypothesis, then… Conclusion

How do you make a Counter Example?

Page 9: If-Then Statements. A statement in two parts Hypothesis and Conclusion. Written in the If-Then form If..Hypothesis, then… Conclusion

You would Negation the conclusion.

Negation is writing the negative or opposite of the statement.

X = 20, negation x ≠ 20NEVER NEGATE THE HYPOTHESIS

How do you make a Counter Example?

Page 10: If-Then Statements. A statement in two parts Hypothesis and Conclusion. Written in the If-Then form If..Hypothesis, then… Conclusion

Since Mr. Grosz go to a High School every week day, then he must be a high school student.

Negation: Mr. Grosz is not a High School student.

The Hypothesis is still true.

THE HYPOTHESIS MUST ALWAYS STAY TRUE

Page 11: If-Then Statements. A statement in two parts Hypothesis and Conclusion. Written in the If-Then form If..Hypothesis, then… Conclusion

The Converse is the switching of the hypothesis and the conclusion.

If the statement was “If p, then q”, then it becomes “If q, then p”.

If x = 3, then x + 4 = 7. The Converse

If x + 4 = 7, then x = 3

Converse is more then a Shoe!

Page 12: If-Then Statements. A statement in two parts Hypothesis and Conclusion. Written in the If-Then form If..Hypothesis, then… Conclusion

If x = 3, then 2x + 4 = 10 Original Conditional

If x ≠ 3, then 2x + 4 ≠ 10 InverseTo find the Inverse; Negate the Hypothesis and the Conclusion. In this example both this statement are True.

If you Negate the Original Conditional Statement you have the Inverse

Page 13: If-Then Statements. A statement in two parts Hypothesis and Conclusion. Written in the If-Then form If..Hypothesis, then… Conclusion

The Contrapositive is the negation of the conclusion and hypothesis of the converse.

If x = 3, then 2x + 4 = 10 Original Conditional

If x ≠ 3, then 2x + 4 ≠ 10 InverseIf 2x + 4 = 10 ,then x = 3 Converse

If 2x + 4 ≠ 10, then x ≠ 3 Contrapositive

If you Negate the Converse, then you get another type of statement.

Page 14: If-Then Statements. A statement in two parts Hypothesis and Conclusion. Written in the If-Then form If..Hypothesis, then… Conclusion

Statements that are both true or false.

Conditional Statement x = 2, then x2 = 4 True

Inverse x≠2, then x2≠4 False

Converse x2=4, then x = 2 False

Contrapositive x2≠4, then x≠2 True

Equivalent statements

Page 15: If-Then Statements. A statement in two parts Hypothesis and Conclusion. Written in the If-Then form If..Hypothesis, then… Conclusion

The Condition Statement and the Contrapositive are both True.

These statements will always have the same true table.

(Meaning they are both true or false)

The Inverse and the Converse have the same true table.

Which are both True or False?

Page 16: If-Then Statements. A statement in two parts Hypothesis and Conclusion. Written in the If-Then form If..Hypothesis, then… Conclusion

If you feed it, then it will grow.

If you don’t feed it, then it will not grow

If it will grow, then you feed it

If it will not grow, then you did not feed it

Lets review the type of Statements

Page 17: If-Then Statements. A statement in two parts Hypothesis and Conclusion. Written in the If-Then form If..Hypothesis, then… Conclusion

If you feed it, then it will grow.( Conditional statement)

If you don’t feed it, then it will not grow(Inverse)

If it will grow, then you feed it(Converse)

If it will not grow, then you did not feed it(Contrapositive)

Lets review the type of Statements

Page 18: If-Then Statements. A statement in two parts Hypothesis and Conclusion. Written in the If-Then form If..Hypothesis, then… Conclusion

We have had 4 Postulate before what are they?

What is a Postulate?

Postulates about Points, Lines and Planes

Page 19: If-Then Statements. A statement in two parts Hypothesis and Conclusion. Written in the If-Then form If..Hypothesis, then… Conclusion

We have had 4 Postulate before what are they?

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Postulate

Postulates about Points, Lines and Planes

Page 20: If-Then Statements. A statement in two parts Hypothesis and Conclusion. Written in the If-Then form If..Hypothesis, then… Conclusion

Postulates without names

Through any two points there exists exactly one line.

A line contains at least 2 points.

If two lines intersect, then their intersection is exactly one point.

Postulates about Points, Lines and Planes

Page 21: If-Then Statements. A statement in two parts Hypothesis and Conclusion. Written in the If-Then form If..Hypothesis, then… Conclusion

Why do most stools have three legs?

Page 22: If-Then Statements. A statement in two parts Hypothesis and Conclusion. Written in the If-Then form If..Hypothesis, then… Conclusion

Answer

Through any three noncollinear points there exist exactly one plane.

You want a stool to only be only in one plane, why?

A plane contains at least three noncollinear points.

Why do most stools have three legs?

Page 23: If-Then Statements. A statement in two parts Hypothesis and Conclusion. Written in the If-Then form If..Hypothesis, then… Conclusion

If two points lie in a plane, then the line containing the points lie in the plane.

( it nails the line to the plane)

If two planes intersect then their intersection is a line.

2 more Postulates about Points, Lines and Planes

Page 24: If-Then Statements. A statement in two parts Hypothesis and Conclusion. Written in the If-Then form If..Hypothesis, then… Conclusion

Page 75 – 77

# 9 – 17 odd, 18, 20, 22, 29 – 34,

36, 38, 40, 41, 44, 48, 52

Homework


Conditional Statement A conditional statement has two parts, a hypothesis and a conclusion. When conditional statements are written in if-then form, the

2.1 Conditional Statements Conditional Statement – a logical statement with two parts. P, the “if part”, hypothesis Q, the “then part”, conclusion If

Parallel and Perpendicular Lines...Parallel and Perpendicular Lines 143 Conditional Statements Identify the hypothesis and conclusion of each conditional. If 6. If E is on AC , then

By phrasing a conjecture as an if-then statement, you can quickly identify its hypothesis and conclusion

Section 2.2. Conditional statements are logical statements with a hypothesis and conclusion. If an animal is a bird, then it has feathers. HypothesisConclusion

Summary and Conclusion - NBER · 2020. 3. 20. · SUMMARY AND CONCLUSION 1. Summary Statement of Hypothesis The permanent income hypothesis can be summarized in a system of three

THE INQUIRY PROCESS Question Hypothesis Identifying Variables Materials Diagram Procedure Results Conclusion

SEMESTER I EXAM Review A 2011 SHELDON BIOLOGY. Match Parts of Scientific Method Problem Statement Hypothesis Experiment Conclusion If and then… Agree

Hypothesis Testing - JCU Australia · Hypothesis A statement about the population that may or may not be true Hypothesis testing aims to make a statistical conclusion about accepting

DESIGNING AN EXPERIMENT. HYPOTHESIS Form a hypothesis If…Then… If we water the plants with Miracle Grow, then the plants will grow taller

Scientific Method 1. Observation 2. Gather Information 3. Hypothesis 4. Experiment 5. Conclusion

Beginning Question And Research Hypothesis And Experiment Analysis And Conclusion

Hypothesis testing - download.workflow4metabolomics.org€¦ · vancomycin-treated population INTRODUCTION (2) ... •Hypothesis testing = inferential method: extrapolation of conclusion

Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form

000 Discrete Math all slides - cse.psu.edugik2/teach/Discrete_Math-4.pdf · •Form of conditional: “If hypothesis, then conclusion”, equivalently “hypothesis → conclusion”

Scientific Method (simplified) Problem Observations Hypothesis Experiment Data Conclusion Retest

Observation Question Hypothesis Test Hypothesis Result (new hypothesis) Conclusion Leads too…..Scientific Theories (widely tested and accepted

15) 17) 18) 1 2 19) 23) 25) Conditional Statement: A conditional statement has two parts, a hypothesis and a conclusion. If-Then Form: the “if” part

Statements that are Conditional with a hypothesis and a conclusion. The If part of the statement is the Hypothesis, and the Then part of the statement

Author Date. Introduction ◦ Hypothesis ◦ Significance ◦ Definitions ◦ Pathway Methods Results Conclusion Q&A

Hypothesis Conclusion (Geometry 1_4)

Hypothesis Testing Part A - Moreau's Mathmoreaumath.weebly.com/uploads/2/3/9/7/23970294/hypothesis_testi… · hypothesis. Example #4 State a conclusion about the null hypothesis

Propositional Logic Lecture 2: Sep 9. Conditional Statement If p then q p is called the hypothesis; q is called the conclusion “If your GPA is 4.0, then

Section 2-1 Using Deductive Reasoning. If/then statements Called conditional statements or simply conditionals. Have a hypothesis (p) and a conclusion

Conditional Statements M260 2.2. Deductive Reasoning Proceeds from a hypothesis to a conclusion. If p then q. p q hypothesis conclusion

Deductive Reasoning Geometry Chapter 2. Vocabulary Converse-formed by interchanging the hypothesis and the conclusion Statement: If p, then q Converse:

SEMESTER I EXAM Review A 2010 SHELDON BIOLOGY. Match Parts of Scientific Method Problem Statement Hypothesis Experiment Conclusion If and then… Agree

Format (Steps to Follow) Purpose Research Question Hypothesis Materials Procedure Results Conclusion

THE STEPS 6 steps Scientific Method Ask a question Form Hypothesis Test Hypothesis Analyze / Collect Data Draw Conclusion Communicate Results

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 1–7) Then/Now New Vocabulary Example 1:Identify Hypothesis and Conclusion Example 2:Write a

Propositional Logic. Conditional Statement If p then q p is called the hypothesis; q is called the conclusion “If your GPA is 4.0, then you don’t need

Vocabulary conditional statement if-then statement hypothesis conclusion related conditionals converse inverse contrapositive logically equivalent

Bell Work “If x=4, then “ 1)Write the hypothesis 2)Write the Conclusion 3) Write the converse 4)What is the Biconditional?

Identify the hypothesis and the conclusion of each conditional statement

2.2 Write Definitions as Conditional Statements. Conditional Statement A logical statement with a hypothesis and a conclusion. If-then form: “If” part