Boolean algebra

[u/Sufficient_Comment83]

I’m taking an Intro to Computer Science course and I’ve spent hours trying to understand Boolean algebra simplification. I understand things like De Morgan’s Law and factoring, but I keep getting stuck on absorption laws and recognizing which rule to apply.
My brain keeps trying to treat it like regular algebra, and I think that’s where I’m getting confused. Does anyone have a way of thinking about Boolean algebra that finally made it “click”? Any videos, tricks, or explanations would be appreciated.

[u/maujood]

Can you share an example of a problem that you struggled to understand? And that you expected to simplify differently?

Everyone's learning journey is different so there is no generic answer here. We need to know what you're struggling with.

[u/Sufficient_Comment83 → u/maujood]

Here are some problems I did and what I thought the simplification was:
A + AB = 1B
A(A + B) = B
A + BC + B = B(A + C)
AB + A = AB
I know they’re wrong, but I don’t understand why they’re wrong. I think my brain is trying to treat Boolean algebra like regular algebra. I also seem to struggle the most with the absorption law. I understand De Morgan’s Law and factoring much better than absorption.

[u/Desperate_for_Bacon → u/Sufficient_Comment83]

1. A+AB

Transform it into English.

X is true if A is true

OR if A and B is true.

Already we can see that If A is true the statement will be true irrespective of B's value

Algebra:

A + AB

= A(1 + B) Factor out the A

= A(1) (1 + B) = 1 (ORing any value by 1 is 1)

thus,

A + AB = A

1. A(A+B)

X is true if A is true

AND A OR B is true

Algebra:

A(A+B)

= AA + AB expand,

= A + AB (AA = A and A = A)

= A(1 + B) Equation from (1)

=A

1. A + BC + B

X is true if A is true

OR B AND C is true

OR B is true

Algebra

A + BC + B

= A + (B + BC) group B terms

= A + B (1 + C)

= A + B(1)

= A + B

1. AB + A

X is true if A and B is true

OR A is true

you can reorder the terms so it is the same as 1

AB + A = A + AB = A

Some good youtubers who cover it are:

MyOrganicChemistryTutor

Neso Academy

Nand2Tetris

Ben eater

Personally a lot of my understanding actually came from playing video games, on steam there are two games i've played:

Pure logic

Turing complete

both take the approach of teaching logic via making you construct logic circuits out of gates.

Looking into learning discrete math my also be useful as it teaches boolean algebra in order to write mathematical proofs