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Question Number 1675 by hhhggvghhh last updated on 31/Aug/15

scv2{bb3vjhkhbkj} nnmvhkvgj6vvfukfjjkhnkgwqqkin ckkmnbmbjknn

$${scv}\mathrm{2}\left\{{bb}\mathrm{3}{vjhkhbkj}\right\} \\ $$$${nnmvhkvgj}\mathrm{6}{vvfukfjjkhnkgwqqkin} \\ $$$${ckkmnbmbjknn} \\ $$

Answered by 123456 last updated on 31/Aug/15

f_ω (z)=Π_(z_0 ∈ω) (z−z_0 )

$${f}_{\omega} \left({z}\right)=\underset{{z}_{\mathrm{0}} \in\omega} {\prod}\left({z}−{z}_{\mathrm{0}} \right) \\ $$

Answered by 123456 last updated on 31/Aug/15

r=p→q s=(∼p)→(∼q) t=(∼q)→(∼p) p q ∼p ∼q r ∼r s t 0 0 1 1 1 0 1 1 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 1 1 0 0 1 0 1 1 p→q≡(∼q)→(∼p) p q ∼p ∼q p⇔q ∼(p⇔q) (∼p)⇔(∼q) 0 0 1 1 1 0 1 0 1 1 0 0 1 0 1 0 0 1 0 1 0 1 1 0 0 1 0 1 p⇔q≡(∼p)⇔(∼q)

$${r}={p}\rightarrow{q} \\ $$$${s}=\left(\sim{p}\right)\rightarrow\left(\sim{q}\right) \\ $$$${t}=\left(\sim{q}\right)\rightarrow\left(\sim{p}\right) \\ $$$${p}\:\:{q}\:\sim{p}\:\sim{q}\:\:{r}\:\sim{r}\:\:{s}\:\:{t}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\mathrm{0}\:\:\mathrm{0}\:\:\:\:\mathrm{1}\:\:\:\:\:\mathrm{1}\:\:\mathrm{1}\:\:\:\:\mathrm{0}\:\:\mathrm{1}\:\:\mathrm{1}\: \\ $$$$\mathrm{0}\:\:\mathrm{1}\:\:\:\:\mathrm{1}\:\:\:\:\:\mathrm{0}\:\:\mathrm{1}\:\:\:\:\mathrm{0}\:\:\mathrm{0}\:\:\mathrm{1} \\ $$$$\mathrm{1}\:\:\mathrm{0}\:\:\:\:\mathrm{0}\:\:\:\:\:\mathrm{1}\:\:\mathrm{0}\:\:\:\:\mathrm{1}\:\:\mathrm{1}\:\:\mathrm{0} \\ $$$$\mathrm{1}\:\:\mathrm{1}\:\:\:\:\mathrm{0}\:\:\:\:\:\mathrm{0}\:\:\mathrm{1}\:\:\:\:\mathrm{0}\:\:\mathrm{1}\:\:\mathrm{1} \\ $$$${p}\rightarrow{q}\equiv\left(\sim{q}\right)\rightarrow\left(\sim{p}\right) \\ $$$${p}\:\:{q}\:\sim{p}\:\sim{q}\:\:{p}\Leftrightarrow{q}\:\sim\left({p}\Leftrightarrow{q}\right)\:\left(\sim{p}\right)\Leftrightarrow\left(\sim{q}\right) \\ $$$$\mathrm{0}\:\:\mathrm{0}\:\:\:\:\mathrm{1}\:\:\:\:\:\mathrm{1}\:\:\:\:\:\:\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{0}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}\:\:\:\:\: \\ $$$$\mathrm{0}\:\:\mathrm{1}\:\:\:\:\mathrm{1}\:\:\:\:\:\mathrm{0}\:\:\:\:\:\:\mathrm{0}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{0} \\ $$$$\mathrm{1}\:\:\mathrm{0}\:\:\:\:\mathrm{0}\:\:\:\:\:\mathrm{1}\:\:\:\:\:\:\mathrm{0}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{0} \\ $$$$\mathrm{1}\:\:\mathrm{1}\:\:\:\:\mathrm{0}\:\:\:\:\:\mathrm{0}\:\:\:\:\:\:\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{0}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{1} \\ $$$${p}\Leftrightarrow{q}\equiv\left(\sim{p}\right)\Leftrightarrow\left(\sim{q}\right) \\ $$

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