1 / 16

An Introduction to Logic

An Introduction to Logic. Why Logic? A proof of any form requires logical reasoning. Logical reasoning ensures that the conclusions you reach are TRUE - as long as the rest of the statements in the argument are also TRUE . Using Logical Reasoning. For example: All Mustangs are Fords.

talisa
Download Presentation

An Introduction to Logic

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. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. An Introduction to Logic

  2. Why Logic? A proof of any form requires logical reasoning. Logical reasoning ensures that the conclusions you reach are TRUE - as long as the rest of the statements in the argument are also TRUE.

  3. Using Logical Reasoning • For example: • All Mustangs are Fords. This fact can be represented by Venn diagram.

  4. More about the Venn diagram From the Venn diagram, we can also write an ”if-then” statement. If… Then… These If-Then statements are called conditional statements.

  5. If…… then…… • In logical notation, conditionals are written as follows: • If p then q Or p q ( read as “p implies q”)

  6. More about Conditionals • In conditional, the part following the word if is the hypothesis. The part following the then word is the conclusion. • Identify the hypothesis and conclusion: If a car is a Mustang, then it is a Ford.

  7. Example • Write the statement as a conditional. Underline the hypothesis and circle the conclusion. Also draw a Venn diagram for the statement. North Thurston HS is in Washington.

  8. Extending Venn Diagrams • Now consider the following statement: You attend NTHS. By placing YOU into our Venn diagram, what can you logically conclude?

  9. Reversing Conditionals • When you switch the hypothesis and conclusion of a conditional statement, you have the CONVERSE of the conditional. Example: Write the converse of the conditional Conditional: If you have a dog, then you have a pet. Converse:

  10. Inverses of Conditionals • When you negate the hypothesis and conclusion of the conditional statement, you have the INVERSE of the conditional. Example: Write the inverse of the conditional Conditional: If you have a dog, then you have a pet. Inverse:

  11. Contrapositives of Conditionals • When you switch AND negate the hypothesis and conclusions statement, you have the CONTRAPOSITIVE of the conditional. Example: Write the contrapositive of the conditional Conditional: If you have a dog, then you have a pet.

  12. TRUTH OR LIES? • In the previous example, the conditional statement is true. Are the related conditionals true? • Converse? • Inverse? • Contrapositive? • How did you know?

  13. Truth or Lies? • The contrapositive of a true statement is always TRUE, and the contrapositive of a false condition is always FALSE. • The converse and inverse of a conditional are either both TRUE or both FALSE. • An example which proves that a statement is false is a COUNTEREXAMPLE.

  14. Your Turn! Write the converse, inverse, and contrapositive for the conditional. Determine if the statements are true or false. If false, give a counterexample. If you are 16 years old, then you are a teenager.

  15. Logical Chains • Conditional statements that can be linked together are called LOGICAL CHAINS. An example of a logical chain is the children’s series “If you give..” http://www.graves.k12.ky.us/powerpoints/elementary/winaelliott.ppt

  16. Example: • Arrange the following conditionals into a logical chain. Given: • If there is a parade, then fireworks will go off. • If there is July 4th , then flags are flying. • If flags are flying, then there is a parade. Prove: If there is July 4th, then fireworks will go off.

More Related