## keebler01 4 years ago Form the contrapositive: If I do not wash my clothes, then I will have nothing clean to wear. If I have nothing clean to wear, then I did not wash my clothes. If I do not wash my clothes, then I will have something clean to wear. If I wash my clothes, then I will have something clean to wear. If I have something clean to wear, then I washed my clothes. If I have something clean to wear, then I did not wash my clothes.

1. keebler01

if i was wash my clothes, then i will have something clean to wear.

2. polpak

3. Alchemista

I discussed this before. However, I will talk about it again.

4. Alchemista

The contrapositive of $$p \implies q$$ is $$\neg q \implies \neg p$$

5. Alchemista

You can make sense of this intuitively, or by following the rules of modus ponens to prove it rigorously.

6. Alchemista

We will start by identifying the statements $p = \text{ "I washed some clothes"}$$q = \text{ "I have something clean to wear"}$ We have $$\neg p \implies \neg q$$ therefore the contrapositive is $$q \implies p$$

7. polpak

$p: \text{I have nothing to wear}$$q:\text{I did not wash my clothes}$ You have an implication of the form: $p\implies q$ The contrapositive is: $\lnot q \implies \lnot p$ So first what is $$\lnot q$$? "I washed my clothes" What is $$\lnot p$$ "I have something to wear" So the contrapositive of the original would be : If I washed my clothes, then I have something to wear

8. polpak

Or you can start with negated forms and swap them as Alchemista did.

9. Alchemista

10. Alchemista

If I have something to wear, then I washed my clothes.

11. polpak

Oh, bother. I read the wrong statement as the original because of how it's formatted. "If I have nothing clean to wear, then I did not wash my clothes." I thought that was the original implication.

12. Alchemista

Might be a good idea to remove the answer, so as not to confuse the original poster.

13. keebler01

ok i think mine sounds right!

14. polpak

Well operating from the premise I gave, I'm correct. But my correct answer is not the answer to the original poster's question.

15. Alchemista

Keebler01, the correct answer is "If I have something clean to wear, then I washed my clothes."

16. keebler01

i wasright!!!!

17. polpak