- #1

mathrookie

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- TL;DR Summary
- I cannot apply distribution law

I can't understand how absorption law is obtained. I get following steps.##a∨(a∧𝑏) = (a∧⊤)∨(a∧𝑏)##

##=(a∨a)∧(a∨b)∧(⊤∨a)∧(⊤∨b)##

then,

I come up with ##=a∧(a∨b)∧⊤∧⊤## so ##=a∧(a∨b)##

But, I cannot get ##a∧(⊤∨𝑏)##, as shown on here, therefore ##a##.

Can you help me? I cannot obtain ##a∧(⊤∨𝑏)## Some people say in other answers in different questions, it is obtained by distribution law. However, what I got by this is the first equation.

[1]: https://proofwiki.org/wiki/Absorption_Laws_(Boolean_Algebras)

##=(a∨a)∧(a∨b)∧(⊤∨a)∧(⊤∨b)##

then,

I come up with ##=a∧(a∨b)∧⊤∧⊤## so ##=a∧(a∨b)##

But, I cannot get ##a∧(⊤∨𝑏)##, as shown on here, therefore ##a##.

Can you help me? I cannot obtain ##a∧(⊤∨𝑏)## Some people say in other answers in different questions, it is obtained by distribution law. However, what I got by this is the first equation.

[1]: https://proofwiki.org/wiki/Absorption_Laws_(Boolean_Algebras)