© 2004 Charlean Mullikin All rights reserved

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Presentation transcript:

© 2004 Charlean Mullikin All rights reserved

A conditional is a statement that can be written in the If – Then form. If the team wins the semi-final, then they will play in the championship.

If the team wins the semi-final, then they will play in the championship. The “If” part is called the Hypothesis. The “Then” part is called the Conclusion.

Then p q Hypothesis Conclusion If If Then

Practice  Write each statement in the if-then form: 1. The lights go out when lightning strikes the power lines. 2. All squirrels are mammals. 3.Cheerleaders can do stunts. 4. Complementary angles have a sum of 90 . 1. If lightning strikes the power lines, then the lights will go out. 2. If an animal is a squirrel, then it is a mammal. 3. If you are a cheerleader, then you can do stunts. 4. If two angles are complementary angles, then they have a sum of 90 . 5. The product of two odd integers is odd. 5. If two integers are odd, then their product is odd.

p q If Hypothesis Then Conclusion Conditional If Then Conclusion Converse Hypothesis q p ConclusionHypothesis

If the team wins the semi-final, then they will play in the championship. Conditional Converse q p p q If they will play in the championship, then the team wins the semi-final. If the team plays in the championship, then they won the semi-final.

If the team wins the semi-final, then they will play in the championship. Conditional Converse q p p q If the team plays in the championship, then they won the semi-final. Inverse ~ p ~ q If the team does not win the semi-final, then they will not play in the championship. Contrapositive ~ q ~ p If the team does not play in the championship, then they did not win the semi-final.

All tigers are cats. Conditional Converse q p p q If an animal is a cat, then it is a tiger. Inverse ~ p ~ q If an animal is not a tiger, then it is not a cat. Contrapositive ~ q ~ p If an animal is not a cat, then it is not a tiger. If an animal is a tiger, then it is a cat.

If an angle is acute, then it has a measure less than 90. Conditional Converse q p p q If an angle has a measure less than 90, then it is an acute angle. Biconditional p  q If both the conditional and its Converse are true, then it can Be written as a biconditional. An angle is acute if and only if It has a measure less than 90. “if and only if”

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(1) p  q (2) p (3) q Notice how the original Conditional has been Broken apart into two pieces. (Detached)

p  q p q If you pass the driving test, then you will get your license. Brian passed his driving test. Brian got his license.

(1) p  q (2) q  r (3) p  r Notice how all three statements are conditionals with three basic ideas. The repeating part cancels out to give the conclusion.

If you get your license, then you can drive to school. p  q q  r p  r If you pass the driving test, then you will get your license. If you pass the driving test, then you can drive to school.

Identify the p and q Is 2 nd statement another conditional ? If yes, check for syllogism. If no, is it a p? Then check for Detachment. If it is not a conditional and not a p statement, Then there is NO CONCLUSION!