CONDITIONAL STATEMENTSModule 5 Lesson 6

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

LET’S TRY ONE

Use the following statement, write the converse, inverse and contrapositive.

If it has bacon then it is good.

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.

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.

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.

ANSWERS

A rectangle is a quadrilateral but it isn’t a square.

A fish swims and it isn’t a duck.

Leap year