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Complete the following Notes: Conditional Statement ____________________________________________________ _____________________________________________________________ Antecedent _____________________________________________________________ _____________________________________________________________ Conclusion _____________________________________________________________ _____________________________________________________________ Proving Conditionals True _________________________________________________ _____________________________________________________________ Proving Conditional False _________________________________________________ _____________________________________________________________ Instance of a Conditional __________________________________________________ _____________________________________________________________ Counterexample of a Conditional ____________________________________________ _____________________________________________________________ Conditionals & Converses Name:_________ Date:__ Examples: If a figure in convex, then it is an octagon. If a figure is an pentagon then it is a polygon.

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Examples: If a figure is discrete, then it is a line. If a line is dense, then it is vertical. If the equation of line is y = x, then it is oblique. Converse: _________________________________________________ _________________________________________________ Write the converse for each of the four if-then statements above. __________________________________________________________

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Complete the following Notes: Conditional Statement ____________________________________________________ _____________________________________________________________ Antecedent _____________________________________________________________ _____________________________________________________________ Conclusion _____________________________________________________________ _____________________________________________________________ Proving Conditionals True _________________________________________________ _____________________________________________________________ Proving Conditional False _________________________________________________ _____________________________________________________________ Instance of a Conditional __________________________________________________ _____________________________________________________________ Counterexample of a Conditional ____________________________________________ _____________________________________________________________ Conditionals & Converses Name:_________ Date:__ Examples: If a figure in convex, then it is an octagon. If a figure is an pentagon then it is a polygon. Called an if-then statement, either contains the words if-then or can be rewritten to contain them. Also called the hypothesis, is the phrase following the word if (or could follow the word if when rewriting the sentence). Also called the consequent, is the phrase following the word then (or could follow the word then when rewriting the sentence). A conditional is only true if it is ALWAYS true. A conditional is false if it is SOMETIMES or NEVER true. Is an example that is true for BOTH the antecedent/hypothesis and the conclusion/consequent. Is an example that is true for the antecedent/hypothesis and false for the conclusion/consequent.

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Examples: If a figure in convex, then it is an octagon. If a figure is a pentagon then it is a polygon. Think to yourself, can a figure be convex and NOT be an octagon? counter- example instance So the statement, If a figure in convex, then it is an octagon is FALSE. Think to yourself, can a pentagon NOT be an polygon? instance counterexample ? NO So the statement, If a figure is an pentagon then it is a polygon, is TRUE.

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Examples: If a figure is discrete, then it is a line. If a line is dense, then it is vertical. If the equation of line is y = x, then it is oblique. Converse: _________________________________________________ _________________________________________________ Write the converse for each of the three if-then statements above. __________________________________________________________ instancecounterexample So this statement is FALSE By the way, these were examples that were neither instances or counterexamples instancecounterexample So this statement is FALSE By the way, these were examples that were neither instances or counterexamples y=x, instancey=3-x, neithery=2, neitherx=2, neither So this is TRUE

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Converse: _________________________________________________ _________________________________________________ Write the converse for each of the three if-then statements above. __________________________________________________________ The write a converse, switch the phrases (but not the words if-then). If, then a figure is discrete it is a line So the converse is If it is a line, then it is dense

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