Lesson Aim:
How do we recognize converses, inverses, contrapositive & conditional
statements?
Lesson Objectives:
SWBAT
Recognize converses, inverses, contrapositive & conditional statements
CONDITIONAL STATEMENTS
Do Now:
State whether these statements are true.
 If you get 65% on the regents then you will receive a
passing grade.
 If it is raining then it must be sunny.
 If earth is a star then the sun is a planet.
 If a whale is a mammal then the clownfish is a
mammal.
Response to DO NOW
 If you get 65% on the regents then you will receive a passing
grade. TRUE
 If it is raining then it must be sunny. FALSE
 If earth is a star then the sun is a planet. TRUE
 If a whale is a mammal then the clownfish is a mammal
FALSE
Red –True
Blue-False
CONDITIONAL STATEMENT
 A conditional is a compound statement
formed by combining two sentences (or facts)
using the words "if ... then.".
 The part following the if… is the hypothesis
and the part following then is the conclusion.
EXAMPLE
 If a polygon has three sides,
then it is a triangle.
TRUTH TABLE FOR CONDITIONAL
CONVERSE STATEMENT
 The converse of a conditional statement is
formed by interchanging the hypothesis and
conclusion of the original statement.
In other words, the parts of the sentence
change places.
The words "if" and "then" do not move.
EXAMPLE
 If it is a triangle,
then a polygon has three sides.
TRUTH TABLE FOR CONVERSE
INVERSE STATEMENT
 The inverse of a conditional statement is
formed by negating the hypothesis and
negating the conclusion of the original
statement.
In other words, the word "not" is added to
both parts of the sentence.
EXAMPLE OF INVERSE STATEMENT
 If a polygon does NOT have three
sides,
then it is NOT a triangle.
TRUTH TABLE FOR INVERSE
STATEMENT
CONTRAPOSITIVE
STATEMENT
 The contrapositive of a conditional
statement is formed by negating both the
hypothesis and the conclusion, and then
interchanging the resulting negations.
In other words, the contrapositive negates
and switches the parts of the sentence. It
does BOTH the jobs of the INVERSE and the
CONVERSE.

EXAMPLE FOR CONTRAPOSITIVE
If it is NOT a triangle
then a polygon does NOT have three
sides.
TRUTH TABLE FOR
CONTRAPOSITIVE
QUESTION
 Look at the truth table for the Conditional
and the Contrapositive, what do you
notice?

 Look at the truth tables for Converse and
Inverse.

LOGICALLY EQUIVALENT
 WHEN STATEMENT HAVE THE SAME LOGIC
& TRUTH VALUE, THEY ARE SAID TO BE
LOGICALLY EQUIVALENT.
Independent Work Period
 : 20 minutes
Closure
Let’s examine the following, identify the type of statement as conditional,
converse, inverse, or contrapositive and its truth value.
If I am sleeping, then I am breathing.
If I am breathing, then I am sleeping.
If I am not sleeping, then I am not breathing.
If I am not breathing, then I am not sleeping.