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Chapter 2.1-2.3 By: Ben Tulman & Barak Hayut Final Review

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Vocabulary Proof- a convincing argument that something is true Proof- a convincing argument that something is true Conditionals- a logical if-then statement Conditionals- a logical if-then statement Converse- a new conditional where you interchange the hypothesis with the conclusion Converse- a new conditional where you interchange the hypothesis with the conclusion Counter Example- an example which proves that the statement is false Counter Example- an example which proves that the statement is false Hypothesis- in a conditional, the part following the word if Hypothesis- in a conditional, the part following the word if

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Vocabulary Cont. Conclusion- in a conditional, the part following the word then Conclusion- in a conditional, the part following the word then Deduction/Deductive reasoning- the process of drawing logically certain conclusions by using an argument Deduction/Deductive reasoning- the process of drawing logically certain conclusions by using an argument Logical Chain- when three conditionals are linked together Logical Chain- when three conditionals are linked together Biconditional- the resulting if and only if statement (iff) Biconditional- the resulting if and only if statement (iff)

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An Introduction to Proofs Proofs start with things that are agreed on Proofs start with things that are agreed on There are different styles of proofs such as formal proofs and free-form proofs There are different styles of proofs such as formal proofs and free-form proofs Our URL Our URL Our URL Our URL

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Introduction to logic This Euler diagram is a good way to show the following statement This Euler diagram is a good way to show the following statement If a car is a corvette, then it is a Chevrolet. If a car is a corvette, then it is a Chevrolet. This statement is a conditional and if you switch the hypotenuse and the conclusion then a converse would be formed This statement is a conditional and if you switch the hypotenuse and the conclusion then a converse would be formed Corvettes Susans Car Chevrolet Corvettes Susans Car Chevrolet An example of a converse: If it is a Chevrolet, then it is a corvette.

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POP QUIZ!!!!!!!! What is the conditional for the statement: What is the conditional for the statement: When it is cloudy, it will rain. When it is cloudy, it will rain. What is the converse? What is the converse? Make a Euler diagram for the conditional. Make a Euler diagram for the conditional.

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Answers If it is cloudy, then it will rain If it is cloudy, then it will rain If it will rain, then it is cloudy If it will rain, then it is cloudy Cloudy Rain

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Introduction to Logic Cont. An example of a logical chain is: An example of a logical chain is: If a car is a corvette, then it is a Chevrolets. If a car is a corvette, then it is a Chevrolets. Susans car is a Corvette. Susans car is a Corvette. Therefore Susans car is a Chevrolet. Therefore Susans car is a Chevrolet. The If-Then transitive property: The If-Then transitive property: Given: Given: A then B, and B then C A then B, and B then C You can conclude: You can conclude: If A then C If A then C

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Definitions Definitions have a special property when they are written as conditional statements Definitions have a special property when they are written as conditional statements Ex. If the figure is a flopper then it has one eye and two tails Ex. If the figure is a flopper then it has one eye and two tails Which is a smickle? Which is a smickle? Flopper Smickle 1 2

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Definitions Cont. Conditional: If a figure is a flopper, then it has one eye and two tails. Conditional: If a figure is a flopper, then it has one eye and two tails. Converse: If it has one eye and two tails, then it is a flopper. Converse: If it has one eye and two tails, then it is a flopper. Notice that both the original conditional and its converse are true, this special property is true for all conditionals Notice that both the original conditional and its converse are true, this special property is true for all conditionals

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