inverse, converse and contrapostitive

[patti72458]

If the remote control is not within my reach, then I will watch the same channel all night.


This is what I come up with for contrapositive: If you do not watch the same channel all night, then the remote control is not within my reach.

Is this correct?

thanks

 

[tkhunny]

Two things wrong:

1) How would you know what I watch?
2) You did not negate the remote control part.

 

[soroban]

Hello, Patti!

Tkhunny is correct.
You switched from "I" to "you" . . . and your contrapositive is wrong.


\(\displaystyle \text{If }\underbrace{\text{the remote control is not within my reach}} \text{, then} \underbrace{\text{ I will watch the same channel all night.}}\)
. . . . . . . . . . . . . . . . . .\(\displaystyle p\) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . \(\displaystyle q\)

Contrapositive:

\(\displaystyle \text{If }\underbrace{\text{I do not watch the same channel all night}} \text{, then } \underbrace{\text{the remote control is within my reach.}}\)
. . . . . . . . . . . . . . . . . \(\displaystyle \sim q\) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . \(\displaystyle \sim p\)