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**Examples: If a figure in convex, then it is an octagon. **

Conditionals & Converses Name:_________ Date:__ Complete the following Notes: Conditional Statement ____________________________________________________ _____________________________________________________________ Antecedent _____________________________________________________________ Conclusion _____________________________________________________________ Proving Conditionals True _________________________________________________ Proving Conditional False _________________________________________________ Instance of a Conditional __________________________________________________ Counterexample of a Conditional ____________________________________________ 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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**A conditional is only true if it is ALWAYS true.**

Conditionals & Converses Name:_________ Date:__ Complete the following Notes: Conditional Statement ____________________________________________________ _____________________________________________________________ Antecedent _____________________________________________________________ Conclusion _____________________________________________________________ Proving Conditionals True _________________________________________________ Proving Conditional False _________________________________________________ Instance of a Conditional __________________________________________________ Counterexample of a Conditional ____________________________________________ 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. 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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**? Think to yourself, “can a figure be convex and NOT be an octagon?”**

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?” instance counter- example 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 ? NO counterexample So the statement, If a figure is an pentagon then it is a polygon, is TRUE.

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**So this statement is FALSE**

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. __________________________________________________________ So this statement is FALSE instance counterexample By the way, these were examples that were neither instances or counterexamples So this statement is FALSE By the way, these were examples that were neither instances or counterexamples counterexample instance So this is TRUE y=3-x, neither y=2, neither y=x, instance x=2, neither

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**The write a converse, switch the phrases (but not the words if-then).**

_________________________________________________ Write the converse for each of the three “if-then” statements above. __________________________________________________________ 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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2.2 Conditional Statements Objective: Students will analyze statements in if-then form and write the converse, inverse, and contrapositive of if-then statements.

2.2 Conditional Statements Objective: Students will analyze statements in if-then form and write the converse, inverse, and contrapositive of if-then statements.

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