Paul Clapham wrote:I don't think that is correct. I do think that DeMorgan's laws would be useful here:
! (A & B) = !A  !B
! (A  B) = !A & !B
Well I used DeMorgan's laws here and the way I did it was as follows:
!(!B && (A  B)) becomes
!!B && (!A && !B) however 2 'nots' become a positive so that becomes
B && (!A && !B) please correct me if I'm wrong // That is where I went wrong I originally put !A  !B
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Practice mindfully by doing the right things and doing things right.— Junilu
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 1
!(!B && (A  B))
you should simplify the interior before applying DeMorgan's law.
Look at !B && (A  B)
This is true if "(B is false) and (either A is true or B is true)". It is then easy to see that this breaks down to "B is false, and A is true".
So then the original becomes !(!B & A). Then apply DeMorgans law on this simpler expression.
Paul Clapham wrote:
Naziru Gelajo wrote:Well I used DeMorgan's laws here and the way I did it was as follows:
!(!B && (A  B)) becomes
!!B && (!A  !B) ...
Then that's definitely wrong. The law says !(X & Y) = !X  !Y, and you didn't apply it right.
Yah I edited my original comment. I mean to put !!B && (!A && !B) which becomes B && (!A && !B) but I can't find a means to get past that. Now I'm looking at another boolean logic expression and this time it has to do with (C  B  A) && B. I can't find any laws that apply to this particular scenario. But from what I can see, There are rules that apply to two variables and definitely not 3 that have a similar structure. Please kindly correct me if I'm wrong.
Naziru Gelajo wrote:
!(!B && (A  B)) becomes
!!B && (!A  !B) ...
...
Yah I edited my original comment. I mean to put !!B && (!A && !B) which becomes ...
!(!B && (A  B)) does NOT become !!B && (!A && !B)
You are taking shortcuts. To avoid confusion, you can do this:
Let X = !B
Let Y = (A  B)
Therefore,
!(!B && (A  B)) ==> !(X && Y)
Now, apply DeMorgan's Laws to !(X && Y). Once you have done that, substitute (!B) for X and (A  B) for Y. Then you can proceed.
Practice only makes habit, only perfect practice makes perfect.
Practice mindfully by doing the right things and doing things right.— Junilu
[How to Ask Questions] [How to Answer Questions]
P ∧ (Q ∨ R) ≡ (P ∨ Q) ∧ (P ∨ R)
P ∨ ¬P ≡ T
P ∧ T ≡ P
Applying DeMorgan's law afterwards becomes much simpler.
The mind is a strange and wonderful thing. I'm not sure that it will ever be able to figure itself out, everything else, maybe. From the atom to the universe, everything, except itself.
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