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I've looked everywhere on the web, in my note and to fellow student without any of them able to explain to me. Here is my question to you.

I can't figure out how to calculate this boolean expression

Can you help me solve : ¬(¬x+x¬y) (sorry i don't know LAtex nor can post image.)

I know that the answer is ¬(x+y) or ¬x¬y

Chax
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The idea is to note that $$1+\neg y=1,$$ so $$\neg x=\neg x(1+\neg y)=\neg x+\neg x\neg y.$$ Can you take it from there?

P.S.: The answer isn't what you think.

Cameron Buie
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  • Are you sure that the answer is not that, the teacher gave us the answer on a answer sheet – Chax Sep 10 '15 at 01:13
  • Yes.${}{}{}{}{}$ – Cameron Buie Sep 10 '15 at 01:20
  • I think i got it. Thank you very much – Chax Sep 10 '15 at 01:28
  • What did you end up with? – Cameron Buie Sep 10 '15 at 01:28
  • I ended up with ¬x¬y. I went to see my teacher and he did a demo for me. What did you end up with? This thing got me confused a bit. – Chax Sep 14 '15 at 00:29
  • Well, using the fact I mentioned, $$\begin{array}\neg(\neg x+x\neg y) &= \neg(\neg x+\neg x\neg y+x\neg y)\ &= \neg\bigl(\neg x+(\neg x+x)\neg y\bigr)\ &= \neg(\neg x+1\neg y)\ &= \neg(\neg x+\neg y)\ &= \neg\bigl(\neg(xy)\bigr)\ &= xy.\end{array}$$ – Cameron Buie Sep 14 '15 at 00:40
  • I get it now, i see where i did a mistake. At the end i forgot one ¬ in the expression ¬(¬(xy)) – Chax Sep 14 '15 at 01:00
  • If it had been $\neg(xy),$ that would have been the same as $\neg x+\neg y,$ not $\neg x\neg y.$ Is the original expression correct? It still surprises me that your teacher's answer key doesn't match. – Cameron Buie Sep 14 '15 at 01:15
  • I wrote it badly. xy is negative. my bad... – Chax Sep 14 '15 at 13:43