How Do We Use Contrapositives?

 

Contrapositives:

Contra- prefix meaning "against" or "opposite"

you negate AND switch the hypothesis and conclusion (inverse and converse)

 

 

Examples:

1. "If I study, then I'll pass geometry." = "If I don't pass geometry, then I didn't study."

     2.  "If I am tired. then I will go to sleep." = "If I don't go to sleep, then I am not tired."

 

The "if" and "then" don't change with the hypothesis and the conclusion.

   

     3. "If Lisa sells the house, than her income will not remain the same." = "If her income does stay the same, then Lisa won't sell the house."

    

    4. "If a number is divisible by six, than it is divisible by three." = "If a number isn't divisible three, then it isn't divisible by six."