Conjunctive/disjunctive normal form

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  • #1
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Let's say I have p<-> q.. how do I get the disjunctive and conjunctive normal form ? I think I'd have to apply DeMorgan to get one of them. I don't know. Can anybody please explain this to me?
 

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  • #2
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p<->q = (p [tex]\wedge[/tex] q) [tex]\vee[/tex] (~p [tex]\wedge[/tex] ~q)
=(p [tex]\wedge[/tex] q) [tex]\vee[/tex] (~p [tex]\wedge[/tex] ~q) [tex]\vee[/tex] (p [tex]\wedge[/tex] ~p) [tex]\vee[/tex] (q [tex]\wedge[/tex] ~q)
=(~p [tex]\vee[/tex] q) [tex]\wedge[/tex] (~q [tex]\vee[/tex] p)

So, the form in red is DNF, while the form in blue is CNF.
 

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