Conditional statements
Download
1 / 16

Conditional Statements - PowerPoint PPT Presentation


  • 207 Views
  • Uploaded on

Conditional Statements. Section 2-2. Objective. Students will be able to recognize conditional statements and their parts to write converses, inverses, and contrapositives of conditionals. Conditional Statements. If-then statements are called conditional statements.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Conditional Statements' - donald


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

Objective
Objective

Students will be able to recognize conditional statements and their parts to write converses, inverses, and contrapositives of conditionals.


Conditional statements1
Conditional Statements

If-then statements are called conditional statements.

The portion of the sentence following if is called the hypothesis. The part following then is called the conclusion.

p q (If p, then q)


p

q

If it is an apple, then it is a fruit.

Hypothesis – It is an apple.

Conclusion – It is a fruit.

A conditional can have a truth value of true or false.



Converse q p
Converse q p

The converse statement is formed by switching the hypothesis and conclusion.

If it is an apple, then it is a fruit.

Converse: If it is a fruit, then it is an apple.

The converse may be true or false.


Underline the hypothesis and circle the conclusion for each conditional statement, then write the converse.

  • If you are an American citizen, then you have the right to vote.

  • If a figure is a rectangle, then it has four sides.


Write each sentence as a conditional statement. conditional statement, then write the converse.

  • A point in the first quadrant has two positive coordinates.

    If a point is in the first quadrant, then it has two positive coordinates.

  • Thanksgiving in the U.S. falls on the fourth Thursday of November.

    If it is Thanksgiving in the U.S., then it is the fourth Thursday of November.


Using a venn diagram to illustrate a conditional1
Using a Venn Diagram to illustrate a conditional conditional statement, then write the converse.

Illinois Residents

Chicago Residents

If you live in Chicago, then you live in Illinois.


Get a partner
Get a Partner! conditional statement, then write the converse.

  • Each of you need to write 5 conditional statements and draw 5 venn diagrams

  • Trade papers

  • Write the converse of each conditional statement your partner wrote.


Biconditionals
Biconditionals conditional statement, then write the converse.

  • Remember: If your original conditional statement is true and your converse is true, then you can write a biconditional. p↔q read as “p if and only if q” we can shorten it to “p iff q”.

  • When either or both of your condition and the converse is false, then you must write a counter example. Why is it false?

  • See page 78 for sample problems! 


The new stuff for today: conditional statement, then write the converse.

negation – the denial of a statement (the opposite)

Ex. “An angle is obtuse.”

Negation – “An angle is not obtuse.”


Inverse p q
Inverse ~p ~q conditional statement, then write the converse.

An inverse statement can be formed by negating both the hypothesis and conclusion.

If it is an apple, then it is a fruit.

Inverse: If it is not an apple, then it is not a fruit.

The inverse may be true or false.


Contrapositive q p
Contrapositive ~q ~p conditional statement, then write the converse.

A contrapositive is formed by negating the hypothesis and conclusion of the converse.

If it is an apple, then it is a fruit.

Contrapositive: If it is not a fruit, then it is not an apple.

The contrapositive of a true conditional is true and of a false conditional is false.


Truth table
Truth Table conditional statement, then write the converse.

T

F

T

T

T

F

T

T

T

T

F

T

T

T

F

T

T

F

F

F

T

T

T

F

T T

T F

F T

F F

Which columns are congruent? These are called equivalent statements, because they have the same truth values!


Assignment
Assignment: conditional statement, then write the converse.

  • P. 93 (15-45) x’s of 3

  • Ask me about the OPTIONAL project!


ad