证明下列布尔恒等式：

A . 1700年 B . 1727年 C . 1737年 D . 1773年

设S={a,b,c}是一个集合,且<img src='https://img2.soutiyun.com/ask/2021-02-03/981199484988802.png' />是S的幂集代数,<img src='https://img2.soutiyun.com/ask/2021-02-03/981199501660756.png' />是二阶布尔代数,映射 <img src='https://img2.soutiyun.com/ask/2021-02-03/981199509691215.png' /> 试证明g是一个布尔同态。

<img src='https://img2.soutiyun.com/ask/2021-01-13/979386185716281.png' />

设n为正整数,证明不等式<img src='https://img2.soutiyun.com/ask/2020-12-12/976625365926413.png' />.

<img src='https://img2.soutiyun.com/ask/2021-02-25/983103268676467.png' />

证明对任何nXn的布尔矩阵A,成立<img src='https://img2.soutiyun.com/ask/2021-02-03/981207788949761.png' />这里Ⅰ是单位矩阵.进而证明,对任何正整数<img src='https://img2.soutiyun.com/ask/2021-02-03/981207807051797.png' />.再证明包括自身可达的可达性矩阵P

<img src='https://img2.soutiyun.com/ask/2020-08-17/966519866012407.png' />

<img src='https://img2.soutiyun.com/ask/2020-09-14/968966909120971.png' />

试证明下列逻辑恒等式(方法不限): <img src='https://img2.soutiyun.com/ask/2021-01-21/980080827718427.png' />

试证明，在任何一个有限布尔代数<img src='https://img2.soutiyun.com/ask/2021-02-03/981200458763499.png' />中，原子的个数必定与反原子的个数相等。

<img src='https://img2.soutiyun.com/ask/2020-12-16/976958738338061.png' />

<img src='https://img2.soutiyun.com/ask/2020-10-12/97136417947982.png' />

<img src='https://img2.soutiyun.com/ask/2020-09-14/968966896570254.png' />

<img src='https://img2.soutiyun.com/ask/2020-08-03/965292956827993.png' />

设<img src='https://img2.soutiyun.com/ask/2021-01-18/979825414936649.png' />是(0，+∞)内的单调减少函数，证明：对任何满足λ+μ=1的正数入，μ及x∈(0，+∞)有下列不等式成立： <img src='https://img2.soutiyun.com/ask/2021-01-18/979825452031771.png' /> 并由此证明：对任何正数a，b，有下列不等式成立： f(a+b)≤f(a)+f(b).

<img src='https://img2.soutiyun.com/ask/2021-01-10/979154285328055.png' />

证明<img src='https://img2.soutiyun.com/ask/2021-01-28/980697697392064.png' />在什么条件下等式成立？

<img src='https://img2.soutiyun.com/ask/2020-11-13/97413809281022.png' />