Artificial intelligent assistant

Equality in Boolean Algebra Say, $$A = C \lor (C\land D) = C \land(1\lor D) = C$$ $$A = C \lor (C\land D) = (C\lor D)\land(C\lor C) = C\land(C\lor D)$$ Now, the part I don't understand here is if we equate we get: $$C \land (1\lor D) = C \land (C \lor D)$$ Which would imply: $$C = 1$$ I have a feeling you can't equate like that in boolean algebra, but I'm not sure. Could anyone explain this result. Thanks

I don't really understand what you did in the first line (the second line looks like an application of the distributive laws for boolean algebra), but in any case, it looks like you're trying to "cancel" from both sides of an equation involving $\land$ and $\lor$. You can't do that. To take an even simpler example: Both $A = A \land A$ and $A = A \land 1$ are true. Equating, you get $$A \land A = A \land 1.$$ Everything okay so far. But you can't proceed from here to "cancel" $A$ from both sides to get $A=1$. A cancellation is usually justified by the presence of an inverse operation (e.g. the inverse of addition is subtraction, so we can subtract $a$ from both sides of $a+b=a+c$ to get $b=c$). There's no inverse for $\land$ or $\lor$ in Boolean algebra.

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