1 × × 1
0 LA?A?A?B1?B2?A?B1?B2 LB?LA?A?B1?B2?A?B1?B2?
____________________3.1.2 用逻辑代数证明下列不等式 (a)
A?AB?A?B
A?BC?(A?B)(A?C)，得
由交换律 (b)
A?AB?(A?A)(A?B)?A?B
ABC?ABC?ABC?AB?AC
ABC?ABC?ABC?A(BC?BC?BC)?A(C?BC)?A(C?B)?AB?AC (c)
A?ABC?ACD??C?D?E?A?CD?E
A?ABC?ACD??C?D?E?A?ACD?(C?D)E_____?A?CD?CDE?A?CD?E3.1.3 用代数法化简下列等式 (a)
AB(BC?A)
AB(BC?A)?ABC?AB?AB (b) (A?B)(AB)
(A?B)(AB)?AB
(c) (d)
_______ABC(B?C)
_______ABC(B?C)?(A?B?C)(B?C)?AB?BC?AC?BC?C?AB?C_____
A?ABC?ABC?CB?CB_____
A?ABC?ABC?CB?CB?A?C
(e) (f)
____________________________AB?AB?AB?AB____________________________
_________AB?AB?AB?AB?A?A?0____________________________________________________________________________
(A?B)?(A?B)?(AB)?(AB)
___________________________________________________________________________________________________________(A?B)?(A?B)?(AB)?(AB)?(A?B)?(A?B)?(AB)?(AB)?(AB?BA?B)(AB?AB)?B(AB?AB)?AB
(g) (h)
(A?B?C)(A?B?C) (A?B?C)(A?B?C)?A?B
ABC?ABC?ABC?A?BCABC?ABC?ABC?A?BC?A?ABC?BC?A?BC?BC?A?C_____________________________ (i)
AB?(A?B)
__________AB?(A?B)?AB?(A?B)?(A?B)(A?B)?A?B
________________________ (j)
B?ABC?AC?AB
(k)
B?ABC?AC?AB?B?ABC?AC?B?AC?ACABCD?ABD?BCD?ABCD?BC
(l)
__________________________________________________ABCD?ABD?BCD?ABCD?BC?ABC?ABD?B(CD?C)?ABC?ABD?B(C?D)?ABC?ABD?BC?BD?B(AC?AD?C?D)?B(A?C?A?D)?AB?BC?BD__________________________________________________AC?ABC?BC?ABC
____AC?ABC?BC?ABC?(AC?ABC)?(B?C)?(A?B?C)?(ABC?ABC)(A?B?C)?BC(A?B?C)?ABC?BC?BC (m)
_______________