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## By Gwendolyn Strasberg

### Integrated Math II - Section 2

Conditional: If you buy a Bentley car, then you are wealthy.

• Truth Value: True

Inverse: If you do not buy a Bentley car, then you are not wealthy.

• Truth Value: False
• Counterexample:  You could choose to spend your money on charity.

Converse: If you are wealthy, then you buy a Bentley car.

• Truth Value: False
• Counterexample: You could be wealthy and buy a Rolls Royce instead.

Contrapositive: If you are not wealthy, then you do not buy a Bentley car.

• Truth Value: True

Conditional: If you are a woman, then you can only open Del Monte Ketchup bottles.

• Truth Value: False
• Counterexample: You could be a capable woman who can open her own Ketchup.

Inverse: If you are not a woman, then you can not only open Del Monte Ketchup Bottles.

• Truth Value: False
• Counterexample: You could be a man and not be able to open any Ketchup bottles.

Converse: If you can only open Del Monte Ketchup bottles, then you are a woman.

• Truth Value: False
• Counterexample: You could be a woman and be able to open many Ketchup bottles.

Contrapositive: If you can not only open Del Monte Ketchup bottles, then you are not a woman.

• Truth Value: False
• Counterexample: In most cases, the ability to open Ketchup bottles is not dependent on gender.

Conditional: If you drink soda as a baby, then you will be happy and popular.

• Truth Value: False
• Counterexample: Jessica Biel was never allowed to have sugary soda as a kid, however she is a happy and popular actress.

Inverse: If you do not drink soda as a baby, then you will not be happy and popular.

• Truth Value: False
• Counterexample: I never drank soda as a baby but I am very happy and have friends.

Converse: If you are happy and popular, then you drank soda as a baby.

• Truth Value: False
• Counterexample: People could be happy and popular because of other reasons such as physical appearance, personality, loving family, and much more.

Contrapositive: If you are not happy and popular, then you did not drink soda as a baby.

• Truth Value: False
• Counterexample: Some people are not happy or popular for many reasons, it could be caused by depression, tragedy, and many other reasons.