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.

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

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- 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.) - 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) - 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.)