I know how can I exapand expression with two variables and two brackets, but how can I expand this:
$$(A ∧ B ∧ C) ∨ (D ∧ E ∧ C) ∨ (D ∧ B ∧ F)$$
In result should be 27 disjunctions and only three variables.
How to expand three boolean brackets with three variables?
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linear-algebra
logic
boolean-algebra
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1Use associativity of $\vee$ and $\wedge$. – 2017-02-22
1 Answers
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Group the first two terms like so:
$$[(A ∧ B ∧ C) ∨ (D ∧ E ∧ C)] ∨ (D ∧ B ∧ F)$$
Expand what is in $[\cdots]$ first, and then combine with the $\lor (D\land B\land F)$ term.
Technically speaking, $\lor$ is a binary operator, which means it takes two inputs, so the expression needs some kind of grouping symbols. However, we simplify notation by dropping the parentheses, similar to how we write $a+b+c$ and not worry about if it's $(a+b)+c$ vs $a+(b+c)$ in most contexts since they have the same value.