The inverse of a conditional statement is found by taking the "NOT" of both statements. Our original "if p, then q" becomes "if not p, then not q."

Let's start with the conditional statement: If it is Tuesday, then it is a weekday.
     p (hypothesis) = it is Tuesday        q (conclusion) = it is a weekday.

The inverse will be: If it is not Tuesday, then it is not a weekday. (Not True)

Conditional Statement: If a number is divisible by 10, it is divisible by 5.
Inverse: If a number is not divisible by 10, then it is not divisible by 5. (True)

Conditional Statement: If you are driving a car, then you must have a driver's license.
Inverse: If you are not driving a car, then you must not have a driver's license. (Not True – maybe you are carpooling)

The contrapositive is found by taking the "NOT" of the converse statement. The converse "if q, then p" becomes "if not q, then not p."

Let's start with the conditional statement: If it is Friday, then it is a payday.
    p (hypothesis) = it is Friday       q (conclusion) = it is payday

The converse will be: If it is payday, then it is Friday.

The contrapositive will be: If it is not payday, then it is not Friday. (Not True)

Conditional Statement: If the polygon is a quadrilateral, then the sum of the angles is 360°.
(Converse: If the sum of the angles of a polygon is 360°, then the polygon is a quadrilateral. (True)

Contrapositive: If the sum of the angles of a polygon is not 360°, then the polygon is not a quadrilateral. (True)

In your notes, write the inverse and contrapositive statement for each conditional statement and determine if it is a true statement.

1. If you are running, you must be a member of the track team.
2. If a triangle has one right angle, then it is a right triangle.
3. If you are a math teacher, then you love your job.

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Check Your Answer

1. Inverse: If you are not running, then you must not be a member of the track team. (Not True – You could be competing in the high jump event.)
   Contrapositive: If you are not a member of the track team, then you must not be running. (Not True – You could be running for pleasure.)
2. Inverse: If a triangle does not have one right angle, then it is not a right triangle. (True)
   Contrapositive: If it is not a right triangle, then it does not have one right angle. (True)
3. Inverse: If you are not a math teacher, then you do not love your job. (Not True – Lots of people love their jobs.)
   Contrapositive: If you do not love your job, then you are not a math teacher. (Not True – Lots of people do not like their jobs.)