I have many sets containing three values like $\{1, -2, 5\}$. I am want to write in mathematical form to filter set where exist one value with different sign. (and for sure, none of them should be zero)
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On
How about ($\mathcal M$ is your family of sets) $\mathcal M \cap \left(F_1 \cup F_2 \cup F_3\right)$, where: $$F_1 = \{\{a,b,c\} : a,b \in \mathbb R_+, c \in \mathbb R_-\} \\ F_2 = \{\{b,c,a\} : a,b \in \mathbb R_+, c \in \mathbb R_-\} \\ F_3 = \{\{c,a,b\} : a,b \in \mathbb R_+, c \in \mathbb R_-\}. \\ $$
Note that you want to filter the sets where not all values have the same sign, that is there exists values of both signs, and zero does not occur. If now $\mathcal A$ denotes your collection of sets, then the filtered collection, which contains only the sets that fulfill your condition is $$ \mathcal F = \{A \in \mathcal A \mid \forall a \in A: a\ne 0 \land \exists a \in A : a < 0 \land \exists a \in A : a > 0 \} $$