Why is this not correct?

[K.I.L.E.R]

U = union
U! = intersection
! = not, or when used with a set, means complement, which means not.


Universal set = {1, 2, 3, ..., 8, 9, 10}
A = {1, 2, 3, 4, 5}
B = {2, 4, 6, 8, 10}
C = {3, 6, 9}

!B U (A U! C)

Expansion 1:
(!B U A) U (!B U C)

Why is this not correct?

Expansion 2:
(!B U! A) U (!B U! C)

Correct.

Reason I asked:
x(a - b) = xa - xb;

You may have just noticed this right now, and in fact I have answered my question:

'x' doesn't keep it's '*' symbol when it's expanded.
It's not:

xa * xb, that's wrong!

Point of post:
This is confusing.

 

[_xxx_]

AFAICR intersection was U mirrored vertically.

 

[StefanS]

U = union
U! = intersection
! = not, or when used with a set, means complement, which means not.


Universal set = {1, 2, 3, ..., 8, 9, 10}
A = {1, 2, 3, 4, 5}
B = {2, 4, 6, 8, 10}
C = {3, 6, 9}

!B U (A U! C)

Expansion 1:
(!B U A) U (!B U C)

Why is this not correct?

Expansion 2:
(!B U! A) U (!B U! C)

Correct.

Point of post:
This is confusing.

That's why:
!B U (A U! C)=(distributive law)= (!B U A) U! (!B U C)=(inverting)=(!B U! A) U (!B U! C)

EDIT: distributive!!!

 

[K.I.L.E.R]

Could you please explain this further?
I don't take notes in class because I thought the book would help.

 

[StefanS]

Could you please explain this further?
I don't take notes in class because I thought the book would help.

Well, since you only recently started university, I am restricting myself to a simple case.

Rules of Set-logic:

(1) Commutativity (warning: requires commutative sets!!!)
A U B = B U A; A U! B = BU! A
(2) Associativity:
A U (B U C) = (A U B) U C; same for U!
(3) Distributivity:
A U (B U! C)= (A U B) U! (A U C); etc.

That's basically all you need.

Last step:
(!B U A) U! (!B U C)=!![(!B U A) U! (!B U C)]=![(!B U! A) U! (!B U! C)]=(!B U! A) U (!B U! C)

!!=1

This last step might require a closed set (which you got anyway).

 

[K.I.L.E.R]

Thanks.

 

[StefanS]

Thanks.

You're welcome! I do everything for the favourite forum weirdo

 

[cristic]

Thanks.

You're welcome! I do everything for the favourite forum weirdo

I wouldn't go *that* far!

 

[Beafy]

In case it helps: There is a homomorphism between sets and boolean logic.
This means you can use stuff like De Morgan and I personally think much better in terms of logic than in terms of sets...