题库网
#6c71aea4-6507-4818-99a9-01da87be4536基础解答题集合新定义问题集合与常用逻辑用语

16.对于集合E={a1E=\{a_{1}a2a_{2}\ldotsa100}a_{100}\}的子集X={ai1X=\{{a_{i_1}}ai2{a_{i_2}}\ldotsaik}{a_{i_k}}\},定义XX的"特征数列"为x1x_{1}x2x_{2}\ldotsx100x_{100},其中xi1=xi2==xik=1{x_{i_1}}={x_{i_2}}=\ldots ={x_{i_k}}=1,其余项均为0,例如子集{a2\{a_{2}a3}a_{3}\}的"特征数列"为0,1,1,0,0,\ldots,0.
(1)子集{a1\{a_{1}a3a_{3}a4a_{4}a5}a_{5}\}的"特征数列"的前四项和等于 [ 3 ];
(2)若EE的子集PP的"特征数列" p1p_{1}p2p_{2}\ldotsp100p_{100}满足p1=1p_{1}=1pi+pi+1=1p_{i}+p_{i+1}=11i991\leqslant i\leqslant 99EE的子集QQ的"特征数列"为q1q_{1}q2q_{2}\ldotsq100q_{100},满足q1=q_{1}=