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Is it possible to write this in a smaller form: $(A \neq \emptyset) \vee (B \neq \emptyset)$ ? is it for example mathematically correct to write it as: $A \vee B \neq \emptyset$ ?

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Are these sets, and are you talking about empty set? Then can write as $A\cup B \ne \emptyset$. –  André Nicolas Apr 2 '12 at 15:24

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I assume that $A,B$ here are some sets. Then it is not correct to write $A\vee B\neq \emptyset$, because $\vee$ is not a set operation. $(A\neq \emptyset) \vee (B\neq\emptyset)$ is a logic statement, which is true if and only if $A\neq \emptyset$ or $B\neq \emptyset$, so $(A\neq \emptyset) \vee (B\neq\emptyset)\Leftrightarrow A\cup B\neq \emptyset$

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Of course, $A \cup B \neq \varnothing$ might be the shorter form you want... –  Johannes Kloos Apr 2 '12 at 15:24

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