Conditional Converse Inverse Contrapositive

Conditional Statements cont.

Lesson 2

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Do Now

Directions: Write the statement below in the conditional if-then form.

On Thursdays bowling is half price.

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Write the converse of the conditional if-then statement.

If it is Thursday, then bowling is half price.

Lesson Objectives

• Find a truth value of a conditional statement and create a truth table.

• Determine what the inverse and contrapositive of a conditional if-then statement is.

• Identifying biconditional statements.

Review from Thursday

A conditional statement is a statement that is written in the if-then form.

The part that follows the if is your hypothesis.

The part that follows the then is your conclusion.

Ex.

If it is dark outside, then it is night.

Review from Thursday

The converse of a conditional if-then statement exchanges the hypothesis and the conclusion.

Ex.

If-then statement: If it is dark outside, then it is night.

Converse: If it is night, then it is dark outside.

Inverse of a Conditional Statement

The inverse of a conditional if-then statement is the negation of the hypothesis and conclusion of a conditional statement.

To negate a statement, is to give the opposite of the original statement.

Original statement: If you are a guitar player, then you are a musician.

Inverse statement: If you are not a guitar player, then you are not a musician.

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What is the negation of the following statement?

The car is red.

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What is the inverse of the conditional if-then statement?

If a dog is a Great Dane, then it is large.

Contrapositive of a Conditional Statement

The contrapositive of a conditional if-then statement is negating and reversing the hypothesis and conclusion of a conditional statement.

Ex.

Original Statement: If you are a guitar player, then you are a musician.

Contrapositive: If you are not a musician, then you are not a guitar player.

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What is the contrapositive of the conditional if-then statement?

If a dog is a Great Dane, then it is large.