- 证明题2.证明(1)A
- 2.证明 (1) A-(B-)=(A-B)︶(A︵C)
(2) (A-B)︶(C-B)=(A︶C)-b
3.设x?0,y?0,x不等于y,证明(x+y)lnx+y/2
- 2.用A+B表示A∨B,AB表示A∧B,A'表示非A.
(1) A-(B-C)
=A-BC'
=A(BC')'
=A(B'+C)
=AB'+AC
=(A-B)︶(A︵C).
(2)(A-B)︶(C-B)
=AB'+CB'
=(A+C)B'
=(A︶C)-B.
3.设f(x)=xlnx+ylny-(x+y)ln[(x+y)/2],00,
∴f'(x)<=f'(y)=-1,
∴f(x)↓,
f(x)>f(y)=2ylny-2ylny=0,
∴命题成立。