1. The number of proper subsets of the set $A=\left\{x \in \mathbf{Z} \mid \log _{2} x \leqslant 2\right\}$ is ( ).
(A) 7
(B) 8
(C) 15
(D) 16
一, 1. C.
From the problem, we know that $x>0, x \leqslant 2^{2}=4(x \in Z)$.
Therefore, $x=1,2,3,4$.
Hence, the answer is $2^{4}-1=15$.