2.1 Conditional Statements

2.1 Conditional Statements

If-Then Statements

A statement in two parts Hypothesis and Conclusion.

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

Conditional Statement

“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

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

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

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

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

How do you make a Counter Example?

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?

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

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 ConverseIf x + 4 = 7, then x = 3

Converse is more then a Shoe!

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

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.

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

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?

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

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

We have had 4 Postulate before what are they?

What is a Postulate?

Postulates about Points, Lines and Planes

We have had 4 Postulate before what are they?

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Postulate

Postulates about Points, Lines and Planes

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

Why do most stools have three legs?

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?

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 75 – 77

# 9 – 17 odd, 18, 20, 22, 29 – 34,

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

Homework