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Let $p = (a \land b) \lor (c \land d)$ where $\land$ and $\lor$ are bitwise AND and OR operators respectively. Can $p$ be simplified?

amWhy
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Anant
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  • It depends what you mean by "simplified", which is a rather relative term. It is currently in disjunctive normal form, and can not be simplified in that form. However, it is equivalent to $(a \lor c) \land (a\lor d) \land (b\lor c) \land (b\lor d)$ (distributive law, twice applied) puts it in conjuctive normal form. – amWhy Aug 12 '20 at 16:06

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Since the expression is sensible on every value (for example, if $b$ is true and $c \land d$ is false, then we need $a$ to know if the full expression is true or false) and it already uses each value only one time, we can't simplify it.

Lucas Resende
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