keebler01 Group Title 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. 2 years ago 2 years ago

1. keebler01 Group Title

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

2. polpak Group Title

3. Alchemista Group Title

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

4. Alchemista Group Title

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

5. Alchemista Group Title

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

6. Alchemista Group Title

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 Group Title

$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 Group Title

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

9. Alchemista Group Title

10. Alchemista Group Title

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

11. polpak Group Title

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 Group Title

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

13. keebler01 Group Title

ok i think mine sounds right!

14. polpak Group Title

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 Group Title

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

16. keebler01 Group Title

i wasright!!!!

17. polpak Group Title