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

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Presentation transcript:

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

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.

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’.

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.

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.

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