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I am solving a question where I have to convert $(\neg P \ \lor Q)$ this equation into principal disjonction normal form. so far I know that to convert it I have to multiply 1 with it. ie; $(\neg P \ \lor Q) \land T$, where $T$ is true. now in the solution of the question after multiplying the equation with 1 it is written like this. $(\neg P \ \lor Q) \land (\neg P \ \lor P)$. so my question is why $(\neg P \ \lor P)$ is coming why can't we write $(P \ \lor \neg Q)$ instead.

fonfonx
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Atanu Mondal
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1 Answers1

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$(P \ \lor \neg P)$ is exactly true. I guess the solution wants to express the normal form uniquely with elements of the original logical proposition (i.e $P$ and $Q$), and avoids using other symbols (such as $T$). This is why they are using $(P \ \lor \neg P)$.

Moreover, note that $(\neg P \ \lor Q) \land (P \ \lor \neg Q) \neq (\neg P \ \lor Q)$. For example, take $P$ False and $Q$ True.

fonfonx
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  • where are you getting those exact negation symbol from I don't have that symbol on my keyboard. By the way thanks for the edit and the elaborated explanation. – Atanu Mondal Jul 23 '17 at 03:08
  • @AtanuMondal you should have a look at latex (https://math.stackexchange.com/help/notation) :) to do the exact negation symbol I type $\neg$. Btw by clicking on edit below my answer you can see exactly what I typed. – fonfonx Jul 23 '17 at 03:11