4

I've been working through the book First Course in Mathematical Logic by Patrick Suppes and Shirley Hill. I'm trying to determine if I'm misunderstanding DeMorgan's law, or there is simply a typo in the book's examples.

My understanding is that the conversions between sentences can be made by the following three steps...

  1. Convert between disjunction and conjunction
  2. Negate each symbol in the conjunction/disjunction
  3. Negate the whole formula

The book provides the following example, with step 1 being the premise, and 2 being the output of applying those steps for DeMorgan's law

  1. $\lnot(P \land Q)$
  2. $P \lor \lnot Q$

It looks like a typo to me, as I would expect

  1. $\lnot(P \land Q)$
  2. $\lnot P \lor \lnot Q$

Is my understanding correct, or am I misunderstanding the steps? Thanks!

MacRance
  • 994
DoubtingThomas3005
  • 43

2 Answers2

5

Yes, you are correct, and this seems to be a typo in the book.

Eric M. Schmidt
  • 3,717
2

There should be a typo indeed. Since $\neg (P \wedge Q) \iff \neg P \vee \neg Q $ can easily be verified using the truth table.

MPHIRI
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