2-3 Conditional Statements

Ms. Andrejko2-3 Conditional StatementsReal Life

If you would like to speak to a representative press 0 nowVocabularyConditional Statement- a statement that can be written in if-then form If-then statement- is of the form if p, then qHypothesis- the phrase immediately following the word ifConclusion- the phrase immediately following the word thenRelated Conditionals- other statements that are based on a given conditional statementLogically equivalent- Statements with the same truth valuesNotationp q = if p, then qp = hypothesisq = conclusion

Conditional Truth Tablepqp qTTTTFFFTTFFTExamplesIdentify the hypothesis and conclusion:

If 3x+4=-5, then x=-3

If you take a class in television broadcasting, then you will film a sporting eventHypothesis: 3x+4=-5Conclusion: x=-3Hypothesis: Take a class in television broadcastingConclusion: Film a sporting eventPracticeIdentify the hypothesis and conclusion:

If you purchase a computer and dont like it, then you can return it within 30 days.

If x+8 = 4, then x= - 4Hypothesis: purchase a computer and dont like itConclusion: return it within 30 daysHypothesis: x+8=4Conclusion: x= -4ExamplesWrite each statement in if-then form:

Those who do not remember the past are condemned to repeat it.

Adjacent angles share a common vertex and a common side

IF you do not remember the past, THEN you are condemned to repeat it.IF 2 angles are adjacent, THEN they share a common vertex and common side.PracticeWrite each statement in if-then form:

A polygon with four sides is a quadrilateral.

An acute angle has a measure less than 90.

IF a polygon has four sides, THEN it is a quadrilateralIF an angle is acute, THEN its measure is less than 90.ExamplesDetermine the truth vale of the following conditionals:

If a and b are negative, then a + b is also negative.

If you have five dollars, then you have five one-dollar bills.

T T = TT F = FCounterexample: you have 1, $5 bill.PracticeDetermine the truth vale of the following conditionals:

If two angles are supplementary, then one of the angles is acute.

If I roll two six-sided dice and sum of the numbers is 11, then one die must be a five.

T F = FCounterexample: 90 and 90 - neither are acuteT T = T5+6 = 11FOLDABLEINSIDE CONDITIONAL TABHypothesisIf-Then StatementConclusionVocabularyConverse- formed by exchanging the hypothesis and conclusionInverse- formed by negating the hypothesis and conclusion of the conditionalContrapositive- formed by negating the hypothesis and conclusion of the converseq p~p ~q~q ~pIMPORTANT NOTE**** NOTE:

The conditional and its contrapositive are logically equivalentThe converse and inverse are logically equivalent

ExamplesWrite the converse, inverse, and contrapositive of each statement:If 89 is divisible by 2, then 89 is an even number

If an animal is a lion, then it is a cat that can roarConverse: If 89 is an even number, then 89 is divisible by 2.Inverse: If 89 is not an even number, then 89 is not divisible by 2. Contrapositive: If 89 is not an even number, then 89 is not divisible by 2.Converse: If an animal is a cat that can roar, then it is a lion.Inverse: If an animal is not a lion, then it is not a cat that can roar. Contrapositive: If an animal is not a cat that can roar, then it is not a lion.ExamplesWrite the converse, inverse, and contrapositive of each statement:If you are 15 years old, then you are eligible to drive.

If the temperature is freezing, then precipitation falls as snow.Converse: If you are eligible to drive, then you are 15 years old.Inverse: If you are not 15 years old, then you are not eligible to drive. Contrapositive: If you are not eligible to drive, then you are not 15 years old.Converse: If precipitation falls as snow, then the temperature is freezing.Inverse: If the temperature isnt freezing, then the precipitation does not fall as snow. Contrapositive: If precipitation doesnt fall as snow, then the temperature isnt freezing.FOLDABLEINSIDE CONDITIONAL TABConverseContrapositiveInverse