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Inference rules 1

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Match the inference with the corresponding law.

	Direct reasoning	Indirect reasoning	Hypothetical syllogism	Disjunctive syllogism
$\var{latex(prop1)} \to \var{latex(prop2)} \\ \var{latex(prop1)}$ __________________ $\therefore \var{latex(prop2)}$
$\var{latex(prop5)} \to \var{latex(prop6)} \\ \var{latex(prop6)} \to \var{latex(prop7)}$ __________________ $\therefore \var{latex(prop5)} \to \var{latex(prop7)}\\\\\\\\$
$\var{latex(prop3)} \to \var{latex(prop4)} \\ \lnot\var{latex(prop4)}$ __________________ $\therefore \lnot \var{latex(prop3)}\\\\\\\\$
$\var{latex(prop3)} \lor \var{latex(prop6)} \\ \lnot\var{latex(prop3)}$ __________________ $\therefore \var{latex(prop6)}\\\\\\\\$

Expected answer:

	Direct reasoning	Indirect reasoning	Hypothetical syllogism	Disjunctive syllogism
$\var{latex(prop1)} \to \var{latex(prop2)} \\ \var{latex(prop1)}$ __________________ $\therefore \var{latex(prop2)}$
$\var{latex(prop5)} \to \var{latex(prop6)} \\ \var{latex(prop6)} \to \var{latex(prop7)}$ __________________ $\therefore \var{latex(prop5)} \to \var{latex(prop7)}\\\\\\\\$
$\var{latex(prop3)} \to \var{latex(prop4)} \\ \lnot\var{latex(prop4)}$ __________________ $\therefore \lnot \var{latex(prop3)}\\\\\\\\$
$\var{latex(prop3)} \lor \var{latex(prop6)} \\ \lnot\var{latex(prop3)}$ __________________ $\therefore \var{latex(prop6)}\\\\\\\\$

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