Question

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

Answer 1

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?

Answer 2

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

Answer 3

i might be completely wrong, its been a while.

Answer 4

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

Answer 5

~( 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!

Answer 6

brb

Answer 7

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

Answer 8

ima go get my book lol >.>

Answer 9

ok

Answer 10

im back!

Answer 11

joe how would u write in ur own words?

Answer 12

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

Answer 13

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

Answer 14

ok

Answer 15

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

Answer 16

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

Answer 17

@ Joe i thnk i got it thanks!

Answer 18

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