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I have problems with CNF form of formula in boolean logic. I need to get it using only laws of boolean algebra.

The formula is:

$$(!a \land !b \land !c) \lor (!a \land !b \land d) \lor (b \land c \land !d) \lor (a \land c \land !d)$$

Thank you for your help guys!

Graham Kemp
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Peter L
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1 Answers1

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To get you started: $(!a \land !b \land !c) \lor (!a \land !b \land d) \lor (b \land c \land !d) \lor (a \land c \land !d) \\ \Updownarrow \qquad\text{Distribute} \\ ((!a\land !b)\land(!c\lor d))\lor ((b\lor a)\land(c\land !d)) \\ \Updownarrow\qquad\text{DeMorgan}\\ (!(a\lor b)\land(!c\lor d))\lor ((b\lor a)\land !(!c\lor d)) \\ \Updownarrow\qquad\text{use }(!P\land Q)\lor(P\land !Q)\iff (!P\lor !Q)\land(P\lor Q)\\ (!(a\lor b)\lor !(!c\lor d))\land ((b\lor a)\lor (!c\lor d)) $

Can you take it from here?

Graham Kemp
  • 129,094