Module 5 Lesson 6

1. CONDITIONAL
STATEMENTS
Module 5 Lesson 6

2. THE STATEMENTS
 The original conditional statement is “ p -> q”
 This is read as “if p then q.”
 p is the hypothesis and q is the conclusion
 Converse q->p
 Inverse ~p->~q. (~ means not)
 Contrapositive ~q->~p

3. LET’S TRY ONE
 Use the following statement, write the converse, inverse and
contrapositive.
 If it has bacon then it is good.

4. ANSWERS
 Converse: If it is good then it has bacon.
 Inverse: If it doesn’t have bacon then it isn’t good.
 Contrapositive: If it isn’t good then it doesn’t have bacon.

5. SOME THINGS YOU NEED TO KNOW
 If the conditional statement is true, then the contrapositive is true.
 If the conditional statement is false, then the contrapositive is
false.
 A counterexample is something that disproves the statement.

6. NAME A COUNTEREXAMPLE
 If a shape is a quadrilateral then it is a square.
 If an animal swims then it is a duck.
 If it is February then it only has 28 days.

7. ANSWERS
 A rectangle is a quadrilateral but it isn’t a square.
 A fish swims and it isn’t a duck.
 Leap year