2.
\((1)\)命题“\(a\),\(b∈R\),若\(|a-1|+|b-1|=0\),则\(a=b=1\)”用反证法证明时应假设为________.
\((2)\)已知函数\(f\left( x \right)=a\ln x,a\in R\),若曲线\(y=f\left( x \right)\)与曲线\(g\left( x \right)=\sqrt{x}\)在交点处有共同的切线,\(a\)的值是_________.
\((3)\)给出下列四种说法:
\(①-2i\)是虚数,但不是纯虚数;
\(②\)两个复数互为共轭复数,当且仅当其和为实数;
\(③\)已知\(x\),\(y∈R\),则\(x+yi=1+i\)的充要条件为\(x=y=1\);
\(④\)如果让实数\(a\)与\(ai\)对应,那么实数集与纯虚数集一一对应.
其中正确说法的为______.
\((4)\)若集合\(A_{1}\),\(A_{2}\),\(…\),\(A_{n}\)满足\(A_{1}∪A_{2}∪…∪A_{n}=A\),则称\(A_{1}\),\(A_{2}\),\(…\),\(A_{n}\)为集合\(A\)的一种拆分,已知:
\(①\)当\(A_{1}∪A_{2}=\{a_{1},a_{2},a_{3}\}\)时,有\(3^{3}\)种拆分;
\(②\)当\(A_{1}∪A_{2}∪A_{3}=\{a_{1},a_{2},a_{3},a_{4}\}\)时,有\(7^{4}\)种拆分;
\(③\)当\(A_{1}∪A_{2}∪A_{3}∪A_{4}=\{a_{1},a_{2},a_{3},a_{4},a_{5}\}\)时,有\(15^{5}\)种拆分;\(……\)
由以上结论,推测出一般结论:
当\(A_{1}∪A_{2}∪…∪A_{n}=\{a_{1},a_{2},a_{3},…{{a}_{n+1}}\}\)时,有_____种拆分.