1. Given the sets $U=\{1,2,3,4,5,6,7,8\}, A=\{1,2,3,4,5\}, B=\{4,5,6,7,8\}$, the number of subsets of set $U$ that are not subsets of set $A$ and are not subsets of set $B$ is
The number of subsets of set $U$ is $2^{8}=256$, the number of subsets of set $A$ is $2^{5}=32$, and the number of subsets of set $B$ is $2^{5}=32$, among which the sets that are subsets of both $A$ and $B$ are $2^{2}=4$.

Therefore, the number of sets that are neither subsets of set $A$ nor subsets of set $B$ is $256-32-32+4=196$.