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\newcommand{\lequiv}{\Leftrightarrow} %equivalence as logical connective
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\begin{document}

{\bf Automated Reasoning - Exercises, WS 2017\\
Homework 1, given Nov 8, due Nov 29}

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1. Discover the sequent rule for ``Modus Tollens'' by using other sequent rules.

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2. Discover the rule for the situation when the negation of one assumption occurs at the first level in a disjunctive assumption,  by using other sequent rules.

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3. Discover the rules for the equivalence (in assumptions, in goal) 
 by using other sequent rules.

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4. Prove:
$$((A \aand B) \impl C)\ \lequiv\ ((A \impl C) \oor (B \impl C))$$
by truth table, by reducing it to CNF, and by sequent calculus.

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