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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.

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For example: All Mustangs are Fords. This fact can be represented by Venn diagram.

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

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

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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.

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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.

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

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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:

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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:

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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.

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

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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.

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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.

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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

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Arrange the following conditionals into a logical chain. Given: 1) If there is a parade, then fireworks will go off. 2) If there is July 4 th, then flags are flying. 3) If flags are flying, then there is a parade. Prove: If there is July 4 th, then fireworks will go off.

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Conditional Statements. 1) To recognize conditional statements and their parts. 2) To write converses, inverses, and contrapositives of conditionals.

Conditional Statements. 1) To recognize conditional statements and their parts. 2) To write converses, inverses, and contrapositives of conditionals.

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