## keebler01 4 years ago Use De Morgan’s laws to determine whether the two statements are equivalent. ~ (p ∧ q), ~p ∧ ~q

1. joemath314159

its been a while since ive dealt with truth tables and things like it, but when you negate something with a ^ or v in it, dont you switch it to the other?

2. keebler01

hold on im not sure let me look at me txt book!

3. joemath314159

i might be completely wrong, its been a while.

4. joemath314159

i think my book is in my car <.< im to tired to get it lol

5. keebler01

~( p∧q)⇔~ p ∨ ~q by law 1 and this is not equivalent to ~ p ∧ ~ q, since if p is true and q is false, the first statement is true but the second is false. i got this from a website not sure if it correct!

6. keebler01

brb

7. joemath314159

i think thats right. I remember always having to switch the sign when you negate.

8. joemath314159

ima go get my book lol >.>

9. keebler01

ok

10. keebler01

im back!

11. keebler01

joe how would u write in ur own words?

12. joemath314159

if the problem didnt say "using De Morgan's Law", i would just use truth tables to show they arent equivalent.

13. joemath314159

but, since it say that, im looking through my book to see which Law would directly oppose that statement

14. keebler01

ok

15. joemath314159

alright i got it. i'll post a pic in a sec.

16. SaltyPete

by definition, the negation of (p ^ q) is (~p OR ~q), so they are not equivalent

17. keebler01

@ Joe i thnk i got it thanks!

18. joemath314159

...and it looks like we arent able to post pics for the time being =/ bleh. Well, one of de Morgan's Laws is: \[\lnot(p\land q) \Leftrightarrow (\lnot p)\lor (\lnot q)\]