2.设P(A)=P(B)=0.5，P(A∪B)=1，则P(overline(A)cupoverline(B))=_____.

由已知条件 $ P(A) = P(B) = 0.5 $ 和 $ P(A \cup B) = 1 $，利用概率加法公式得： \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \implies 1 = 0.5 + 0.5 - P(A \cap B) \implies P(A \cap B) = 0. \] 根据德摩根定律， \[ \overline{A} \cup \overline{B} = \overline{A \cap B}, \] 故 \[ P(\overline{A} \cup \overline{B}) = P(\overline{A \cap B}) = 1 - P(A \cap B) = 1. \] 答案：$\boxed{1}$