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#1 2016-01-05 11:27:15

Monox D. I-Fly
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Registered: 2015-12-02
Posts: 857

[ASK] De Morgan's Law for 3 Statements

Weeks ago I had a job to edit a mathematic encyclopedia. When I needed to prove something, I did it using steps similar to ~(p ^ q ^ r) ≡ ~p ∨ ~q ∨ ~r. However, when my co-worker which is also a mathematic education graduate just like me doubted me because as far as she knew, De Morgan's law taught at school and college only consisted of two statements yet I applied it to three statements. I have explained that De Morgan's law still applied for three sentences because the two logical operations within the brackets are the same, but she still didn't believe it. Then I went easy on here by replacing that step with another method and showed that after a few steps I still got the same result as before, but she got confused. According to you guys, is De Morgan's law really only applicable to two statements?

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#2 2016-01-05 12:06:00

zetafunc
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Registered: 2014-05-21
Posts: 2,107
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Re: [ASK] De Morgan's Law for 3 Statements

No, De Morgan's law still holds for 3 statements. In fact, it's even applicable to an (uncountably) infinite number of statements. If you're having doubts, just let S = Q ^ R and use De Morgan's law for 2 statements. (Though it sounds like you've already done that.)

Last edited by zetafunc (2016-01-05 12:08:38)

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#3 2016-01-06 02:55:43

Monox D. I-Fly
Member
Registered: 2015-12-02
Posts: 857

Re: [ASK] De Morgan's Law for 3 Statements

Well, this morning I tried to explain that to her. Thankfully she understood my explanation.

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