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Unit 2 Part 1 Conditional, Converse, Inverse, and Contra- Positive Statements

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Terms Conjecture : is an unproven statement that is based on observations. Counterexample : is a specific case for which the conjecture is false. (one example that will make the conjecture false) Conditional Statement : is a logical statement that has two parts, a hypothesis and a conclusion.

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Four types of statements. Conditional: If ‘p’ (hypothesis), then ‘q’ (conclusion). Converse: If ‘q’, then ‘p’. Inverse: If not ‘p’, then not ‘q’. Contrapositive: If not ‘q’, then not ‘p’.

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Example If it is raining outside, then it must be cloudy. ‘p’ hypothesis ‘q’ conclusion Converse: If ‘q’, then ‘p’. If it is cloudy, then it must be raining outside. Inverse: If not ‘p’, then not ‘q’. If it is not raining outside, then it must not be cloudy. Contrapositive: If not ‘q’, then not ‘p’. If it is not cloudy, then it must not be raining outside.

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Biconditional Statement If a conditional and converse are true then you can write a Biconditional Statement. Example. If two lines intersect to form a right angle, then they are perpendicular. If two lines are perpendicular, then they intersect to form a right angle. Two lines are perpendicular if and only if they intersect to form a right angle.

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Mini Project You will now create your own if, then statements to present to the class. Mini Project is due on ????

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