Condandlogic

Geometry Drill 10/7/13Aki, Bard, and Coretta live in

Albany, Biloxi, and Chicago. No one lives in a city that begins with the same letter as her name. Aki writes letters to her friend in Chicago. Who lives in what city? #??

Identify, write, and analyze the truth value of conditional statements.

Write the inverse, converse, and contrapositive of a conditional statement.

Objectives

conditional statementhypothesisconclusiontruth valuenegationconverseinversecontrapostivelogically equivalent statements

Vocabulary

By phrasing a conjecture as an if-then statement, you can quickly identify its hypothesis and conclusion.

VocabularyConditional statementA statement written in the form IF___,THEN___.

If P, then Q.P –> Q (NOTATION)

VocabularyConditional statements:If P, then QP implies QQ, if P

ALL MEAN SAME THING

VocabularyHypothesis-statement following the word “if”.

Conclusion-statement following the word “then”.

FACT OR FICTION???

IF TWO ANGLES ARE SUPPLEMENTARY, THEN THEY ARE BOTH RIGHT ANGLES.

REVERSE THE HYPOTHESIS & CONCLUSION

FACT OR FICTION???

IF TWO ANGLES ARE

RIGHT ANGLES, THEN THEY ARE SUPPLEMENTARY ANGLES.

VOCABULARYCONVERSE- A conditional statement with the hypothesis and conclusion interchanged.

If Q, then P. Q –>P

FACT OR FICTION???

If x = 4, then x2 = 16

Is the converse true?

If x2 = 16, then x = 4.

Write the converse. Is the converse true?

1. If two angles are vertical , then they are congruent.

2. If x > 0, then x2 > 0.

The negation of statement p is “not p,” written as ~p. The negation of a true statement is false, and the negation of a false statement is true.

DefinitionSymbol

sThe converse is the statement formed by exchanging the hypothesis and conclusion.

q p

DefinitionSymbol

sThe inverse is the statement formed by negating the hypothesis and conclusion.

~p ~q

Definition Symbols

The contrapositive is the statement formed by both exchanging and negating the hypothesis and conclusion.

~q ~p

Write the converse, inverse, and contrapositive of the conditional statement. Use the Science Fact to find the truth value of each.

Example 4: Biology Application

If an animal is an adult insect, then it has six legs.

Example 4: Biology Application

Inverse: If an animal is not an adult insect, then it does not have six legs.

Converse: If an animal has six legs, then it is an adult insect.

If an animal is an adult insect, then it has six legs.

No other animals have six legs so the converse is true.

Contrapositive: If an animal does not have six legs, then it is not an adult insect.

Adult insects must have six legs. So the contrapositive is true.

No other animals have six legs so the converse is true.

Write the converse, inverse, and contrapostive of the conditional statement “If an animal is a cat, then it has four paws.” Find the truth value of each.

Check It Out! Example 4

If an animal is a cat, then it has four paws.

Check It Out! Example 4

Inverse: If an animal is not a cat, then it does not have 4 paws.

Converse: If an animal has 4 paws, then it is a cat.

Contrapositive: If an animal does not have 4 paws, then it is not a cat; True.

If an animal is a cat, then it has four paws.

There are other animals that have 4 paws that are not cats, so the converse is false.

There are animals that are not cats that have 4 paws, so the inverse is false.

Cats have 4 paws, so the contrapositive is true.

If-Then Transitive Property (postulate)

Given: If A, then B. If B, then C.

Conclusion: If A, then C.

(logic chain)

If yellow is brown, then red is blue.

If black is white, then yellow is brown.

If red is blue, then green is orange.

If black is white, then yellow is brown.

If yellow is brown, then red is blue.

If red is blue, then green is orange.

Write as a conditional

ALL MATH TEACHERS ARE MEN.

WRITE IN IF-THEN FORM.

IF A PERSON IS A MATH TEACHER, THEN THEY ARE

A MAN.

A VENN DIAGRAM is sometimes used in connection with

conditionals

If p , then q.

q

p

Make a Venn diagram

If Ed lives in Texas, then he lives south

of Canada

Venn DiagramIf Ed lives in Texas, then he lives

south of Canada.

Texas South of Canada

Texas

CounterexampleIf Ed lives south of Canada, then he

lives in Texas.

Texas

South of Canada

Ed lives in Maryland