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{\bf Logic 1, WS 2017.
Homework 2, given Oct 20, due Oct 27}

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\noindent
1.
Prove that
for any propositional formulae
$\varphi_1, \varphi_2, \ldots, \varphi_n, \psi,$
if
$(\varphi_1 \and \varphi_2 \and \ldots \and \varphi_n) \impl \psi$ is valid,
then
$\varphi_1, \varphi_2, \ldots, \varphi_n\ \elc \psi.$

(See the style used in the lecture for proving the opposite implication.)


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\noindent
2.
For implication and equivalence, write the equivalences involving
truth constants and the ones involving one truth constant and one propositional variable.
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\noindent
3. Prove by reducing both sides to CNF:
$$ ((A \and B) \impl C)\ \equiv\ ((A \impl C) \or (B \impl C)).$$

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